That's a great question. I'm not sure I am up to the task.
First, I cannot say for an absolute fact that free will exists. We certainly believe we have freedom of choice, but do we? I have struggled for years to try to define consciousness, without much success. Certainly, our conscious thought convinces us of our own free will. But clearly that wouldn't count as evidence if the cells in our brain are actually operating as deterministic machines at some very low level. But generally, I would make the "unscientific" argument that my consciousness implies my free will.
Second, should indeterminism exist as a necessary requirement for true free will? Possibly, and again I do not think this can be demonstrated as an actual requirement for free will. But let's suppose it is. Is nature indeterministic in some respects? We know about some important physical laws which appear indeterministic - such as QM. But as you know, it may be possible to connect the apparent randomness with unknown initial conditions. Those initial conditions, plus deterministic laws, could actually be a prescription for absolute cause and effect - and then we wouldn't really have free will. I personally choose to believe that the randomness in nature is without prior cause. But again I would not call this a scientific argument.
Thirdly, do animals have free will? Does my dog? Is my dog conscious? I think so, but can I be sure? And if so, at what level of creature - going down the chain - does free will disappear? It certainly gets messy as you move down that slope.
And yet with those arguments made - and they are certainly not very strong ones - I am not sure I am any closer to answering your main question: how would free will work? Perhaps our brain acts like a quantum magnifier. Somehow, a small quantum fluctuation is amplified within our neurons and that gives an unpredictable element to our actions. We call that free will. But even in that case, would it be? Or would a random external stimulus be the culprit, and we are back to being "robots" that act in a knee-jerk reaction to the stimuli we are presented with.
Sticky problem to be sure. I see consciousness and indeterminism as somehow important to the notion of free will, but I can't make get very far without resorting to questionable reasoning - reasoning which involves belief more than knowledge. I certainly don't expect anyone to be persuaded by this.