For time skips, I try to only describe the changes to a character if they've undergone significant ones. Like, I try not to do any time skips unless something big happens in between, anyway. So usually when I pick back up at the tail end of the timeskip I'll let my readers know what happened --- physically and emotionally. Obviously, a character isn't only going to change physically. Well, maybe some might, if they're not affected by whatever happened in between the times at each end of the skip. But as far as my own stuff goes, anyway, I usually only use timeskips when I need to. I actually generally try to avoid writing any 'formally' recognized timeskips (as in, putting "ONE YEAR LATER" somewhere in the story) unless something really significant happened, because otherwise I feel like it will have less of an impact. But that's also just a personal preference.
So honestly for me timeskips can be anywhere from a week to a thousand-plus years. However long it takes for a significant change to occur. When it does, I tend to like describing it from the viewpoint of a character who wasn't tagging along with the protagonists (or whoever I'm focusing on) in the beginning. I feel like it has more impact if I have my protagonist --- let's say he's a goodie two-shoes private school kid --- be described by a third party we haven't met yet (or maybe have, in some cases) as rugged and war-torn, with an intense look of determination in his eyes, or something like that.
Like I said, though, just personal preference, and the way I write my best timeskips. As long as there's a significant change that took place, physically, emotionally, or both, I'd put some sort of timeskip in there and describe just what changed, at least to an outsider's perspective, unless you're sticking with something like a first-person or limited third-person perspective and therefore your own protagonist will be able to let us know exactly what's changed.
I also feel like massive descriptions of what changed aren't necessary. If your character had significant enough of a change, it will be shown through their words and actions after the timeskip. So I don't think one necessarily needs to detail it, but rather have the character show it through their lifestyle choices. If you've fleshed out a character well enough, your readers will be able to tell there's been quite a bit of change, even if you don't spend time detailing exactly what's been changed.