The first stage is to work out how many separate days are shown on screen during the movie. So here's a good old-fashioned list of them:
Day 1: Groundhog Day
Day 2: The first repetition
Day 3: The fixed pencil
Day 4: Punching Ned
Day 5: Deceiving Nancy
Day 6: Robbing the bank
Day 7: Seeing Heidi 2 with a French Maid
Days 8-12: Engineering the near-perfect date
Day 13: The bad perfect date
Days 14-21: One for every slap
Day 22: "Phil you look terrible!"
Day 23: Jeopardy
Day 24: "This is pitiful!"
Days 25-27: Breaking the alarm clock
Day 28: Kidnapping Punxsutawney Phil
Day 29-31: Phil's suicides
Day 32: I'm a God!
Days 33- 35: First piano lessons
Day 36: Sexually harassing Ned
Day 37: Looking after the homeless man
Day 38: The final Groundhog Day
So, by my reckoning that's 38 separate days shown in the movie. This is of course assuming that every separate thing listed above happens on separate days, which I think isn't too much of a dangerous assumption, given that Phil is something of a quitter (case in point: multiple attempts at suicide).
Second, and far more difficult stage is to take things Phil says as indicators for other days we do not see. Jump over to page two to find out how we work that out...