There are 3 decision points during the game of Ultimate Texas Hold'em: Pre-flop, the Turn, & the Showdown.  Below is the perfect strategy for the Pre-flop decision and a simplified strategy for the Turn & Showdown. For the optimal strategy, I have found Stephen How's Ultimate Texas Hold'em strategy to be the most comprehensive. He has great coverage of the game on his site, Discount Gambling. The advice used in this game is modeled after his strategy.

PRE-FLOP (first decision):

When raising, always make a 4x raise. The player should never make a 3x raise.

Your HandStrategy
Pair of 3's or betterraise
Ace + Anyraise
Suited King + Anyraise
Suited Q6 or betterraise
Suited J8 or betterraise
Unsuited K5 or betterraise
Unsuited Q8 or betterraise
Unsuited JT or betterraise
All otherscheck

TURN (second decision):

Your HandStrategy
No Pairalways check
One Pairraise if pair uses one of your cards. check if pair is on the board (community cards).
Two Pairalways raise
Tripsraise if the trips uses one of your cards. check if trips is on the board (community cards).
All hands greater than Tripsalways raise

SHOWDOWN (last decision):

Your hand is better than Tripsalways raise
You have Tripsraise if the trips uses one of your cards or your lowest kicker is a 9. Otherwise, fold
You have Two Pairraise if your 5-card hand is better than the board's 5-card hand, Raise if your kicker is a jack or better. Otherwise, fold
You have a Pairraise if pair uses one of your cards or you have at least a Jack. Otherwise, fold
Scare Board and you have less than a pairalways fold
The board is unpairedraise if you have 2nd nut kicker. Otherwise, fold
The board is pairedraise if you have 3rd nut kicker. Otherwise, fold