Covered in the Complete Arkham FAQ, page 4:
Q: When does an investigator pick up Clue tokens on the
A: Investigators pick up Clue tokens in only two cases:
1. During the Movement Phase, if an investigator ends his movement in an Arkham location or street area containing Clue tokens, he picks them up after evading or combating any monsters in the same location or area. Investigators cannot pick up Clue tokens from a location or street area and then continue moving.
2. During the Mythos Phase, when a Clue token is placed in the same location as one or more investigators, one of them may immediately pick it up. If they cannot agree who gets the Clue token, the first player decides.
Note that investigators do not pick up any Clue tokens when they are sent to a location with a Clue token during the Upkeep Phase, the Arkham Encounters Phase, or the Other World Encounters Phase.