Goofy Casting...
Thought I'd chime in on the whole subject of learning to cast with the "off hand". Of course, it goes without saying that this is a good way of defeating a contrary breeze, and I won't really get into other methods for that here... though that's actually the topic of this post.
I taught myself to cast lefty last year, in about 2 half-hour sessions. Now, I'm no great caster, nor a particularly quick study. I also don't profess to tremendous accuracy with that hand, but it's typically enough to get the job done... and keep from getting whacked by the fly.
I used a version of Lefty Kreh's teaching method that breaks the cast down into separate parts that we can see. He uses this to teach the double-haul, but it works just as well to learn to cast (with either hand). Basically you cast totally side-arm, with the rod parallel to the water. Get out about 30 ft of line in front of you. Sweep the rod back and gradually accelerate until the sudden stop at the end. Now, instead of trying to go directly into the forward cast, let the line drop to the ground. Do the same thing in the opposite direction, again letting the line fall to the ground after the cast. Ideally the line should unroll and lay out straight, with no hook or bend or waves.
In practice it takes a while to get the timing right so the first few casts are awful. However, by watching what happens to the line at the end of each cast, it's amazing how quickly our brains and hands adjust to correct the mistakes. And, if we get confused we can study the movements of our good casting hand.
Make sure you're doing a couple key things if you try this.
1) The rod should be almost totally parallel to the water/ground.
2) Let the line fall to the ground after each section of the cast - both forward and backward.
3) Slow everything down. The slower you do this, the better, and the more you'll learn from each cast.
After a while you'll feel you've got the timing down; try keeping the line in the air for a few false casts. An important note here: once you get the feel of this, don't try keeping the line in the air for a dozen false casts. If you do your hand and arm will naturally tire after the first few casts (especially with the off hand). Once the hand tires it loses it's finess and you'll actually end up practicing poor technique about half the casts. You don't learn to shoot a basketball by starting with three-pointers. Try to limit yourself to 3-4 false casts then let the line fall again. This gives your hand a chance to rest and allows you to assess the quality of the final cast.
I could go further with this. One of the biggest mistakes beginners make when trying to teach themselves to cast is making too many false casts. Their hands tire and they end up frustrated at the end of the session when they could leave feeling they've made progress. The other mistake they make is not practicing for the right amount of time. In this case, too much is just as bad as too little. This has to do with the way we train our muscles. I've heard it said that optimum practice time is 15-20 minutes, though I have no actual evidence to back this up (merely heresay and conjecture... are those are kinds of evidence?). Anyways, the main point the author was making was that our brains and muscles need repetition in order to form the 'habit' of a new physical task. However, the muscles tire quickly and then instead of training new muscles to do a new task, we fall back on the old muscles which perform the new task inefficiently. Basically if we practice for too long we end up learning the wrong series of muscle movements but if we don't practice enough, we have to practically start over next time. Above all, if you don't know how to cast properly, get some instruction (DVD, Books, Magazine, Instructor). Like someone once said, practices doesn't make perfect, it makes permanent.
Good luck.