Make yourself a list
You shouldn't need to spend a whole lot of timie learning an entire new chart. Instead just learn which specific decisions are different from the game you've already learned.
Some examples:
1) If the game allows resplitting aces, just resplit them given the opportunity (no real effort needed to remember this).
2) For a D10 game, you're going to hit rather than double '9' and most soft hands (you'll stand rather than double with A7 against a dealer 6 or less).
3) Learn the half dozen or so hands you'd surrender if it is offered.
4) Learn which pairs should not be split in a no DAS game.
5) Learn the few plays which are different for an H17 game.
6) Learn the plays which are different for 1D and 2D games.
I would recommend that for each rule variation you're likely to encounter, simply make yourself a list of the plays which are different from the game you've learned to play. If you're an experienced player, all decisions from your primary game should be automatic, and you should only need to think about the handful of plays where there is a difference. I have found that simply reviewing my list before playing a session on a table with different rules is sufficient to get me through the session without making serious errors.