After all, soft determinists are determinists, so they believe that our actions are causally determined. How can our actions be regarded as free if they are causally determined?
Essentially, what the compatibilist does is try to redefine free will in such a way that it's compatible with determinism.
For instance, I'm free to choose what I will have for lunch. Within the choices that are possible, there's nothing which actually forces me to choose ham over tuna. The choice is mine and mine alone. Now, my choice might have been influenced by preexisting events and motivations: maybe I don't like tuna, maybe I've got a coupon for my favorite restaurant I'd like to use instead, maybe I'm a vegetarian and will have to skip lunch. But, even though that choice was deterministic, it was still a choice. In that sense, we might call this ability to make choices "free will".
Admittedly, compatibilism can feel like a bit of a cop-out. Rather than worry about what everyone else is worrying about, the compatibilist chooses to shrink their definitions down to fit something much smaller, instead.
Our actions (choices) are completely free.
(I must first make a disclaimer that I'm not interested in the topic of "unobservable determinism", that is when I feel my action is free while "in fact" - from God's or physic's p.o.v. - it was predetermined by atoms or such disposition. Only the case of determinism-in-my-consciousness, i.e. the cause appears to me, presents itself in the setting of my choice - so I blame things for my choice, - can bother me. I must keep agnostic about things bypassing consciousness but claiming that they cause my consciousness. Reasons or causes can exist only for consciousness.)
They are free - which is alias to say that I'm the only author of my choice - because consciousness automatically rejects (negates) the circumstances at the moment of choice. If an armed man points a gun onto you and commands "step back", he and his gun are precisely what your consciousness excludes from determinants when it selects to obey. You will say afterwards in excuse that the gun forced you to step back (i.e. here's a cause), but at the moment of your decision to move back the gun was just the thing you took not to meddle. It was here, pending and frozen, as you did your free decision. The gun was as if waiting for your free decision on the theme of the gun incident.
While the gun was kept in nonbeing, the consciousness chose among 2+ possibilities of itself (yourself). One choice was made, it was spontaneous (it itself wasn't rational, despite that thinking could be included "around" the decision). A possibility exists by mode of nonbeing and thus cannot draw you to it; the gun is also deactivated. Here is complete nothing which decides - and you feel yourself for a moment drifting free in empty space where any side is nobody else's side. Suddenly you're aware of the choice having been just made, from now on the gun is threatening, the man is not joking, and you find yourself doing step back.
Nothing forced you, except yourself who was nothing at the decision of choice among some possibilities apparent to the consciousness. Conditions and thinking can bring forward or conceal possibilities, but there will always be 2+ ones, equally "weight" because they are not, just opportunities of "towards".
If you say not the gun, but rather your instinct of life pushed you back, I'd say, hmm, if the instinct is an unconscious structure (so the action was pure reflex) - see the disclaimer. Else the instinct is for consciousness (and there exists no instinct except consciousness of the instinct) and by this it could be an object like gun, to be disarmed by it in rejection, like gun, or it could be in a form of taste for living, making plans etc. - one of possibilities, to be dim. So choice of any action is an adventure on your own. Covering oneself with causes or reasons or fleeing from the feeling of disappointment about own past decision are self-deceptions.
The view expressed here is different from what @FirstLastname has written in their answer: "My choice might have been influenced by preexisting events and motivations: I don't like tuna, maybe I've got a coupon for my favorite restaurant I'd like to use instead, maybe I'm a vegetarian.... But, even though that choice was deterministic, it was still a choice". To my mind, a choice cannot be deterministic. The thing is that the actual choice I've made - to take tuna, for example - was made free of my own predispositions or customs, and that my preference for tuna is used only as explanation, moreover, it appears as real motive (seen as cause or reason) only thanks to the choice just already done: it is reconstructed here and now from scratch. Motivations cannot preexist.
Free will is a good effective theory for describing how humans behave.
To summarize, an "effective theory" is a theory we can use to describe a system, that works and is accurate, even if it doesn't work when you probe the system at a more fundamental level.
For example, temperature flow, which satisfies the "heat equation", acts like a fluid with partial differential equations describing how a room that's hot at one end and cold at the other, will smoothly flow towards an equilibrium over time. This is a perfectly effective way to describe temperature, yet this is only the statistically most likely thing that will happen. When probing it deeper, you see that this is the result of a bunch of particles that move and collide in certain ways. You would see that there's no fundamental guarantee that the macroscopic properties of a system will evolve in such a way that is compatible with the heat equation, even if you do the experiment 1000 times and find that it's consistent. The heat equation will simply be violated when you probe to a small enough volume at a small enough time scale, and you'll realize that it's only being satisfied at the macroscopic level because that's what tends to happen on average.
Other similar examples are classical electrodynamics to describe how charges work in electric and magnetic fields, or Newtonian gravity to describe how to get into a stable orbit around a foreign planet. Any time you probe deeper, you find that these widely accepted theories of physics are violated. So is that a reason to blow the whistle and tell the world that physicists are wrong? Shouldn't we be changing all the physics classes to tell students the "true" theory? Well... we don't actually know the "true" theory (if that can be properly defined philosophically). The most accurate and advanced modern theory of how the world works, the Standard Model, is something that we know is wrong! (Here, by "wrong", I mean insufficient to explain certain things.)
But even if the Standard Model was the correct, perfect description of the physical world, it still wouldn't be realistic to use for things like, say, biology, sociology, or even some branches of physics. Yes, technically you can derive all of biology from the standard model of physics, but doing so would be such a grand enterprise that it's just not worth it. Nor is it a worthwhile way of seeing the world and developing your epistemology, from the perspective of a biologist. It is useful to describe biology in terms of cells, protein molecules, DNA and RNA, and the way these things tend to behave in relation with each other. An omniscient being might find the biologists' way of describing things to be far too limiting, and prefer to look at a biological system at a more fundamental level. They might, for example, use the Standard Model to determine what will happen in a biological system by calculating the behavior of all the fundamental particles in that system. But, because of our limitations, we cannot adopt the epistemological style of an omniscient being.
If you do want to say that it's all "wrong" (including the Standard Model of particle physics), you have to adopt an unusual epistemological style that we don't usually adopt for most things in our life. If something is only right because it can be perfectly, consistently described by the physical theory that works in all domains of inquiry, then everything we have ever believed or known is wrong. When Isaac Newton discovers the equation for how a satellite orbits a planet, and then uses it to predict how an object in orbit will behave, anyone who says that he is "correct" is bound to a definition of "correct" that allows an effective theory to be correct even if it would turn out to be wrong if probed at a different scale of time or size. I would argue that this is a perfectly good and reasonable way for determining whether something is "right" or "wrong".
For any good effective theory of human beings and how they act, it is useful to describe, and think about each other as beings for whom there is a set of possible actions we can take, and treat the specific actions that we do take as a choice. A choice is made by a source that sees a set of possible actions and selects one. In that sense, "freedom" is just a measure of the volume of possible choices that can be made. Again, an omniscient being would see how all our actions are carried out due to the behavior of all quarks, leptons, gluons, photons, W-bosons and Z-bosons in our body and would see this as a far less limiting way of perceiving things than our "free will" macroscopic model. But, based on the standard that I argued from in the previous paragraph, that doesn't make the latter perspective "wrong".
If you're not satisfied with this answer, then I argue that you shouldn't be satisfied with most of the descriptions we have about the real world. After all, they are all simply effective theories which would be too limiting a description for an omniscient being.
For processes that happen inside and outside of a system, free can mean that the choice-selection made on the inside cannot be forced from the outside. In that, it is 'free' from being directed by outside forces. Insects lack this kind of freedom.
Similarly, assuming human have 'primitive urges' (sleep, eat, reproduce), then free can be to decide to not follow the urge and go for a walk instead. So, it is 'free' from being directed by primitive urges. Many animals lack this kind of freedom.
All this is possible with determinism, and it 'merely' indicates the semantic independence in choice of one system from the rest of the world.
As said before this 'weak' kind of free will still distinguishes humans from many animals (even if all processes were deterministic), and is thus not useless.
A certain degree of determinism is even helpful for this kind of freedom, because in order to e.g. consistently decide not to drink any alcohol for one year, you need a reliable (deterministic) brain that follows that decision.
An interesting answer (with which I only partially agree) is that given by Stephen Wolfram and Daniel Dennett, as summarised here. Essentially, one considers an object to be exercising free will if it's impossible to work out what that object is going to do except by simulating it perfectly.
I recommend reading Chapter 3.2 of the link, where Conway's Game of Life is used as an example: while the Game of Life evolves according to perfectly-specified rules, we still can't (in general) deduce with certainty what any given configuration is going to do over time unless we simply step through the Game and see what happens. The money quote from the article is:
… [deducing with perfect accuracy what is going to happen] is time consuming, in such a way that, by the time you have made the required computation, the world has already evolved…
Here, "has already evolved" means "if you have deduced what is going to happen, then effectively you have made a copy of the game state and evolved it": it is provable that no shortcuts are possible, in general, in the Game of Life. (Proof sketch: implement a universal computer by means of AND and NOT gates, with gliders representing electrons.)