http://www.wgt.com/help.aspx#bracket
Bracket rules. Scroll down a little to the "How are ties handled?" section for a full explanation.
Essentially, there are 11 tiebreakers in 9-hole brackets and 20 tiebreakers in 18-hole brackets before it comes down to the "who posted first" rule. Both players would need to have the exact same card, hole for hole, for the final tiebreaker to come into play. Though it can happen in a 1-on-1 bracket, the probability of it occurring is low.
I recommend reading the whole FAQ when you have some time. It's generally informative.