I have found that putting myself into those pressure situations more often - teeing it up in tourneys of all sorts is essential. It is the same for pros who find themselves in contention for a major but fade having never before experienced the pressure associated with a zillion eyeballs watching your every shot. The stat about Muirfield major winners was telling: no rookie had won there in a major - in fact (I think), I think the only major winners at Muirfield in the Open Championship were all Hall-of-Famers who have experienced the pressure of the moment.
As you place yourself in more pressure situations, you will become more accustomed to the feelings and requirements for good play right from the first tee..Add in all of these other excellent cues: visualization, selecting a key target spot for a shot, developing a routine and simply moving on from a bad shot to the next shot are all essential steps.
And remember, the best hit less than ideal shots ALL THE TIME! Tiger has won more times this year than any other male pro golfer. Yet he also has hit a couple of the most wayward shots televised this year - Splashing balls at the Players and at Liberty National in spots off target that most of hackerdom sees and understands only too well. In both cases he came back, almost pulling out the victory at Liberty National...Let's see, Tiger has played about 1,000,000 tournament pressure rounds in his life...More is better! And author Malcolm Gladwell gathered compelling anecdotal evidence that becoming an expert in anything takes about 10,000 hours of practice!!