There are several things you can try:
First, make sure to do all your upper body work with dumbbells instead of a barbell, as this will force your weaker side to work rather than "go along for the ride" while the strong side pulls more weight (literally and figuratively).
You can do your left side first, doing 1-arm moves, and only do as many with the right side as the left can do. Unfortunately, this may make the right side weaker, so it's not a good option.
Do one-arm curls, starting with the right side. Let's say you can do 10 reps at 12#. Do the same curls, same weight on the left, and when you've reached your limit (let's say 8 reps), you can either 1) do negative reps by using your right hand to help (but only as much as you need) the weight up on the positive part of the move, and lower slowly using just the left arm till you get the full number of reps or 2) take a short break, then do another rep or two, continuing until you hit the goal number of reps.
Another option is to do one more set of exercises for the left than for the right.