First of all, the wind is our enemy in fly casting. It shows all flaws and poor technique. When conditions are perfect you can get away with a lot, add a breeze and things get a lot tougher.
Tip #1 tighten your loop...Many people have been taught or know about stopping their rod at 10 o'clock and and 2. Generally that gives you a decent enough loop to project your fly out where you want it to land. In mildly windy conditions, this may not be enough to hit your target. The wider the loop the more the air effects it. Try tightening up your loop by stopping at 11 and 1. This will create a much tighter loop giving you more power and accuracy. Be careful not to stop to short on either end or you will create a tailing loop which will leave you with either a terrible knot or the line wrapped around the rod. You want your fly line and leader to travel over your rod tip approximately one to two feet. You will be amazed at what this will do to help combat the wind.
The other tip is more of a cheat. The technique is known as a single haul. After you make your backcast, when you start for forecast stroke you pull down on the slack line accelerating the speed of the line and pulling it through the cast. This has a lot to do with timing and you will need some practice to use this consistently. As you begin to accelerate forward pull downward on the line with you left hand (being a right handed caster) and stop your rod abruptly at 1 o'clock. Remember you are casting your line out, not down at the water. I see people all the times forcing the line down onto the water trying to pound the line through the wind and end up sending the trout to a new zip code. It's always a good idea to spend a little bit of time "knocking the rust off" before your trip out west.
Practice when the conditions aren't perfect and you'd be surprised how easily you can adapt when you show up for your trip. 20 minutes three times a week for two weeks will help you immensely and prepare you for most situations that you will encounter.