If two or more teams end up with same points in points table, then team having more Goal Difference i.e., Goals Scored minus Goals Against, wins the title.
if Goal Differences are also same for those teams, then team having more Goals Scored would win the title.
And if Goals Scored are also same for those teams, then all those teams on top having same points, same goal differences and goals scored would compete in a play-off match at a neutral ground. Note that, a play-off match is played only if there is a tie for championship, relegation, or qualification to other competitions. Otherwise tied teams are considered to occupy the same position.
Reference: English Premier League Wikipedia
1. 2011-12 EPL, Manchester City and Manchester United:
Manchester City won the title by having +8 goal difference.
2. 1988-89 EPL, Arsenal and Liverpool:
Arsenal won the league championship on goals-scored, after finishing level on points and goal-difference with Liverpool.