The 2014 ATP Official Rulebook, 9.03 (Emirates ATP Rankings), Section E lists three different tie breakers in the event that players have the same total number of points.
E. Ties. When two or more players have the same total number of points, ties shall be
broken as follows:
1) the most total points from the Grand Slams, ATP World Tour Masters 1000 mandatory tournaments and Barclays ATP World Tour Finals main draws, and if still
2) the fewest events played, counting all missed Grand Slams, ATP World Tour
Masters 1000 tournaments and Barclays ATP World Tour Finals they could have
played (as described under A. above) as if played, and if still tied, then,
3) the highest number of points from one single tournament, then, if needed, the
second highest, and so on.
For example, let's look at the players currently ranked #78 and #79. Both Somdev Devvarman and Alejandro Falla have 662 total points. So the first tie breaker is the total points from Grand Slams, ATP World Tour Masters 1000 and the Barclays ATP World Tour Finals. This information is available on the ATP site:
Somdev Devvarman ratings breakdown:
Alejandro Falla ratings breakdown:
In the tie breaker, Devvarman has 195 points, and Falla has 155 points, so Devvarman is currently ranked ahead of Falla.