For some people there is no good evidence that we do not have free will.
For a review of what evidence there might be, consider Alfred R. Mele's Free: why science hasn't disproved free will. Mele takes a skeptical view of the evidence that we do not have free will.
Some of the types of evidence he considers are the following:
- Libet-style experiments where some decisions could be interpreted to be made unconsciously being generalized to a claim that "people probably never make conscious decisions to do things". (page 24)
- "New-wave Libet-style" neuroscience where people in "fMRI and depth electrode experiments don't make conscious decisions to press buttons or click keys" is generalized to "probably people never make conscious decisions to do things". (page 38)
- Social psychology experiments such as done by Daniel Wegner where some "human actions aren't caused even partly by conscious intentions" is generalized to claiming "no human actions are caused even partly by conscious intentions". (page 49-50).
- "Bold situationist arguments" where it is asserted that "human behavior is entirely driven by the situations in which people find themselves and the effects these situations have on automatic behavior-producing processes." (page 72)
The supposed evidence that we are determined, that is, do not have any free will at all are based on specific experiments that are generalized to all of our behavior. The proof is a matter of faith in the generalization and without that faith, regardless what these experiments show, we have free will.
Even without examining alternate interpretations of what that specific evidence might mean, the generalization to all our actions, to saying that we have no free will whatsoever is a stretch that needs to be filled with something stronger than assertions.
Note that having free will does not require that all of our actions are without constraints of any kind. That is what makes this difficult for those who believe in determinism. It is only the determinist who must make such a strict claim against free will since it is the determinist who claims we do not have this at all.
Let's consider the OP's question: How do I believe in free will?
One way to potentially defeat the belief in determinism would be to take a skeptical approach to the claims that we do not have free will and examine that evidence critically. Mele's book is a short summary that might be a place to start.
In the comments the OP wrote: "Shoot, I might even start believing in an eternal torture chamber of burning flesh."
This issue has nothing to do with any religious position unless one wants to call the determinist master narrative a "religion".
For an atheistic, physicalist perspective on free will that is also critical of the evidence provided by the determinist master narrative see Mark Balaguer's Free Will. He believes it is up to neuroscience to determine whether we have free will or not. It is not up to philosophers. And we are so far from that result we should not expect it in our lifetimes.
Balaguer, M. (2014). Free will. MIT Press.
Mele, A. R. (2014). Free: why science hasn't disproved free will. Oxford University Press.