Well I'm by no means an expert in tournaments, but I've done a fair bit of ring games play and at least understand basic tournament strategy.
The basic difference is the fact that every chip in a tournament is not equal, because survival is rewarded. Your 2nd chip is not worth as much as your 1st, and both are worth more than your 3rd chip. Using this logic, you make plays you would never make in a ring game in a tournament. You could make the case for laying down AA in a tournament, and a lot of the time it's actually profitable to call with trash like 38o. In a cash game it all revolves around ev. Blinds don't change, you can buy in as many times as you want, and all money is equal. So you want to make the plays that net you the most positive ev in the long run. Say you have JJ vs. AK (somehow you see the cards flip over) to a 259 flop late. You don't want to give them a chance to draw out so you probably overbet, hoping for a fold. In a cash game, you want to bet enough to not give them odds
to call (implied odds are big too though, for example if an A or K comes. Basically the strategy should be similar to the very beginnings of a tournament, without the idiots pushing ATC who haven't been knocked out yet, but again you should be happy if you've got your money in with a 60/40 edge, because in the long run you win.
If you are familiar with poker and tournament poker, I'd look at No Limit Hold 'em, Theory and Practice by Sklansky (I think Miller too). He expects you to already understand poker, which it seems you do, and it may take a while to work through all the math if you're not familiar with some of the concepts, but it's definitely a good book for cash games. If you're a good tournament player, you're well on your way to being a good cash games player, but there are a few key differences. Good luck.