Decide if you enjoy betting/gambling. There is nothing wrong with not betting if the process or idea is uncomfortable. Golf is supposed to be enjoyable and there is no reason to bet if that will make the round less fun.
Don't bet more than you are comfortable losing. Determine what you will lose if you lose every bet and hole. That number should be equal to or less than the amount you are willing to lose and not feel bad. For me it is $20. Typically the worst case scenario does not occur and often I win a few bucks. But I have to be ready to lose the whole amount and not hold a grudge.
Understand completely the bet(s) and the rules. Vague descriptions like "USGA Rules except the unreasonable ones" shouldn't fly. You don't want the whole bet riding on the last hole and find out your opponent expects a Mulligan on the last tee.
Have everyone pony up the money upfront and let the most stable person hold on to it and disburse the money after the match. It always amazes me how many people that like to make bets don't seem to have any cash when the payoff time comes. If someone bets a $1.00, I expect them to pay not because I need the $1.00 but because a bet was made.
Finally, resist "playing straight up". When a better player is with 3 golfers of lesser ability, he will typically suggest playing "straight up" because it is easier to figure out and "real golfers" don't want strokes. You wouldn't race Usain Bolt for $20 in a 100 meter sprint "straight up". If a better player won't handicap the match in some way (i.e. use different tees, give strokes, etc...), there is no shame in turning down the bet. I'd rather have a reputation as someone who won't bet than as a sucker.