You will definitely want to check out eHam's sister site Contesting.com at (where else!) http://www.contesting.com/
The most helpful piece of advice I have is to learn the rules of the contest. Probably the most crucial piece of the rules is the exchange. This is the information you have to exchange with the other station. This can be your name, the year you were first licensed, you power level, your age, your state or ARRL section and some even exchange the time of the contact. Many contests also require a consecutive serial number. Also, most contests also require exchanging an RST report. It is a long standing debate as to the validity of this, but 99.9999999999999% of the time, it will always be 59 or 599 for CW and RTTY regardless of how hard it is to hear the other station!
Another very important item in your arsenal is contesting software. At the very simplest level, it will calculate your score and format the final results into the proper format for uploading to the contest organizer which is called "cabrillo" in most cases. More sophisticated software will interface with your radio and automatically plug in the band data so you don't have to worry about it. Some even have the ability to record your voice so you won't go hoarse calling out CQ Contest over and over again! They also have macros for RTTY and CW modes as well. One of the most popular programs is the N1MM Contest Logger at (you guessed it) http://www.n1mm.com
. It is a very robust program with lots of features and has a bit of a steep learning curve. It will take a while to learn it, but it is well worth the time. Bets of all, it is free! I am sure other contributors will share links to their favorite programs as well.
For your first contest, I would advise spending some time listening to hear how others are making exchanges and to get the feeling of the flow of the contest.
Successful contesters take years to perfect their technique. Don't get discouraged! Contesting is an art and it is not something that comes over night.