Well, the techniques really vary. I've given this sort of answer several times in the past, but to save you a search...
Some figures are simply repainted. I might paint only a small area, or I might repaint practically the entire figure. The paint might be applied by hand with a tiny brush, or it might be sprayed from a rattlecan, in which case there's usually lots of masking tape involved.
Other customizers use airbrushes for their paint applications. I have no experience with that.
Some figures are also re-sculpted. My usual material for that is Super Sculpey. If you put Sculpey onto a figure, that's a process called additive sculpting.
Sometimes I use a rotary tool called a dremel to take detail away from a figure. In real-life sculpture, this technique is known as subtractive sculpting, like when an artist sees a block of marble and 'frees' the statue he sees inside it. But when dealing with action figures, the subtractive only does so much. It's usually just an in-between step before also additive-sculpting new details over top of the subtracted areas.
Some figures, like the "Simon Smith" Scooter, are a combination of parts from multiple donor figures: head of Scooter, body of Lew Zealand, top hat from tux Kermit.
And some figures have totally new materials added to them, like the feathers I've added to some of my commission Piggy figures, etc.
And, some figures are entirely sculpted from scratch, like what Christian does. His have no action figure inside them, as mine do.
Yes, boiling makes some plastic softer. It also can warp and melt other plastic, so that technique has limited uses. Sometimes BOTH kinds of plastic are present on one figure, so the boiling technique can't be used.
In short, there are as many ways of doing the custom figures as there are ways of making puppets. Each artist brings their own skills and medium of choice to their projects. I encourage you to experiment and see where the journey of discovery leads you.
You may be the very first person to ever think of the BEST way of doing something, and then we'll all be asking you, "how did you do that?"
Alex