I understand what Autonomy means. However, I fail to understand how it maps on to respect for others.
This is described towards the end of the second section of the Groundwork of the Metaphysics of Morals.
The definition of autonomy is:
Autonomy of the will is the characteristic of the will by which it is a law to itself (4:440)
The link between autonomy and respect for others is the defining core of the concept of what he calls kingdom of ends:
[E]very rational being, as an end in itself, must be able to view itself as at the same time universally legislating with regard to any law whatsoever to which it may be subject, because it is' just this ﬁttingness of its maxims for universal legislation that marks it out as an end in itself; likewise that this dignity (prerogative) it [i.e. a rational being] has above all merely natural beings brings with it that it must always take its maxims from the point of view of itself, but also at the same time of every other rational being as legislating (which are therefore also called persons). Now in this way a world of rational beings (mundus intelligibilis) as a kingdom of ends is possible, and possible through their own legislation of all persons as members. (4:438, bolded mine)
In other words: As autonomy is about the will being a law to itself and is a property of rational beings as such, any "legislating act", i.e. determining how things should be per autonomy, has to consider the autonomy of every other rational being, i.e. their dignity.
This means that the concept of the autonomy of the will itself entails the respect for the autonomy of others, i.e. their dignity, because autonomy is something that pertains to the will of every finite rational being:
[T]he legislation that determines all worth [i.e. autonomy of the will of a finite rational being] must itself have a dignity, i.e. unconditional, incomparable worth, for which the word respect alone makes a beﬁtting expression of the estimation a rational being is to give of it. Autonomy is thus the ground of the dignity of a human and of every rational nature. (4:436)
The reason for why it pertains to every (finite) rational being is beyond the scope of this question, but comes down to the fact that all the analysis of the second section which results in the concept of autonomy started with the concept of the will of a (finite) rational being as such. Thus, autonomy is a concept entailed in the concept of the will of a (finite) rational being and thus trivially pertains to every (finite) rational being. Well, according to Kant's argument, that is.