Sprint:
Sprint was always my favorite round. At nationals, I missed two Targets but still managed to get into the Countdown because of my sprint score (it's also the first tie-breaker). So Sprint is important.
In the actual competition, I didn't follow any of the weird "start at the end" or "skip questions you can't get right away" strategies. I just blazed right through them. I guess part of this was based on my ability; I could do all of the problems (except maybe 1 or 2), it was just about how much time I spent on them. I found it most useful to finish all of the problems I started, unless I really was stuck, which didn't happen much. Anyway, my advice (assuming you get 20+ in practices) is to just go in order. The last ones are the hard ones, and they usually take longer, but all of the problems are worth the same amount, so it's best to make sure you do the easy ones.
At State, the biggest thing I can say about Sprint is to use the problem number to your advantage. If it's a #7, and the best you can come up with is like 20 separate cases, there's probably an easier way. This is also true only slightly of Team, and not at all of Target. On Sprint, the first few should get you warmed up, and I would expect to get half way in around 1/3 the total time.
To prepare, I would just find a hundred or so Sprint problems and work through them all in one or two sittings. Just doing problem after problem after problem helps you for Sprint.
Target:
Target has always been my worst round, except at Regionals. The key with Target is to get an answer quickly, and then check it in every way you know. I always solved both problems (or at least got an answer) and then went back and checked them. Occasionally, I checked the first before moving on, but you're right the first time a lot.
Make sure to read the problems at least twice and remember all of the little tricks they like to throw in, like converting square inches to square feet (x144), and anything else they might come up with.
To be honest, I don't know how to prepare for Target without just doing old tests.
That's all I can think of right now. Confidence is a great booster too, almost as much as sugar and caffeine.
No, I'm serious - lots of sugar helps you think faster. But that's coming from someone who never gets stressed, so it might be different for you. But I always had a pop or two and any donuts they had before the contests.