According to USGA rules...the preferred method of settling ties is through an 18-hole playoff. When that is not possible, the USGA recommends that you "Use last nine, six, three, and finally 18th hole. One half, one-third, one-sixth, one-18th of the handicap should be deducted from the scores on these holes.  Fractions of one-half stroke or more should count as a full stroke; any lesser fractions should be disregarded."  Summarizing the equation...

Equation:

Step 1. GROSS last 9 minus one-half Hcp, if tie continue to Step 2
Step 2. GROSS last 6 minus one-third Hcp, if tie continue to Step 3
Step 3. GROSS last 3 minus one-sixth Hcp, if tie continue to Step 4
Step 4. GROSS 18th hole minus one-eighteenth Hcp

Example:

Assume Dan has a 9 handicap and Joe a 14 handicap.

LAST NINE HOLES
Dan  39 - (9 / 2) = 39-4.5 = 39-5 = 34
Joe  41 - (14 / 2) = 41-7 = 34
TIE

LAST SIX HOLES
Dan 27 - (9/3) = 27-3=24
Joe 29  - (14/3)= 29 - 5 = 24
TIE

LAST THREE HOLES
Dan 12 - (9/6) = 12-2 = 10
Joe  14- (14/6) = 14-2 =12

Dan WINS!