Dan Vasser has no control over when he travels through time. However, he usually has advance warning of when he is about to "travel": He develops a headache. When he feels a headache coming on, Dan quickly moves to a place where his sudden disappearance will not be noticed.
When Dan returns from the past, he reappears at a point in time after his most recent disappearance. The amount of time that elapses between his departure and return varies from a few minutes to a few hours.
Dan can change events in the past without altering the events of his own life. In the pilot, Dan reads in 2007 that someone killed Nicole Gaines and her son Jacob in 1997. After traveling to 1997 and preventing Neal Gaines from taking the life of his wife and son, Dan returns to 2007 and learns that Jacob survived and later saved a group of children. Everything and everyone else around him has, however, remained the same.
It is possible that Dan's actions create alternate timelines, and that his return brings him to the newest "version" of the universe he left. Whether the other, "broken" timelines continue to exist is unclear, but this possibility seems unlikely for at least three reasons.
First, when Dan returns to his present, Katie remembers his most recent vanishing. But if Dan is returning to a completely new timeline, one in which the person he was sent to save is alive and well, there would have been no reason for the Dan in that timeline to have traveled to the past. Consequently, Katie should have no memory of his having vanished. Clearly she does, as illustrated when Dan disappears from the bathroom while Katie is showering in Game Three, leaving his shoes behind -- shoes that Katie later brings to him at the San Francisco Register.
Second, if Dan returns to a newly created timeline, the inhabitants of the other timelines would experiece him as having vanished permanently.
Third, the "repaired" timelines would also have their own Dan Vassers. So if Dan "returns" to a newly created timeline, there should be (at least) one Dan too many. There is no evidence that this is the case.
The simplest explanation is that there is one timeline that is anchored in some way (possibly by Dan and by other travelers), and that Dan can change events around the edges, modifying some elements of the timeline while leaving other elements untouched.
How Dan travels through time is not yet clear. The ripple effect that surrounds him before he disappears hints that there may be some kind of wormhole effect. In the episode Game Three, Dan raids his present-day refrigerator, telling Katie that he's "always hungry" when he gets back, and he doesn't know why. His pre-travel headache and his post-travel hunger both suggest that his traveling is tied in some way to the metabolic processes of his own body -- though not in ways that can be detected by an MRI.
Livia implies to Dan that they have "missions" to complete, which suggests that someone -- or something -- is sending them on those missions. The identity and intent of the guiding agent is, so far, completely unknown.
Dan's mission is limited in scope. Dan is limited to altering lives of people he been assigned to. Dan can't alter lives of other people that he has not been assigned to. Moreover, Livia and possibly other agents are directly interfering to prevent Dan from changing lives of other people that he has not been assigned to. This becomes really clear in 'Game Three', where Dan couldn't save sister of his boss. Livia interfered Dan from saving the sister's life.
One timeline idea has its problem too. It doesn't explain how Dan remembers various histories of different events. There is definite paradox if there is only one timeline. If there is only timeline ,then how does Dan remembers different version of histories? In episode one, he remember a version of history where Nicole and Jacob were killed in 1997. Then he also remembers modified version where Jacob rescues kids in 2006.
Although alternate time line idea has its problem, One timeline idea has definite logical contradiction: a form of grandfather paradox. If Dan saved Jacob Gaines from death, then Dan wouldn't know about that Jacob Gaines was saved. Since Jacob is alive, Dan wouldn't need to go back in time. Then if Dan didn't go back in time, then Dan wouldn't be there to save Jacob Gaines in the first place. Then Jacob Gaines would have die due to lack of Dan's intervention. Then this would prompt Dan to intervene. And so on. This indicates a circular time loop logic where there is no cause and effect. Of course there must be definite cause and definite effect. This is a form of grandfather paradox that one timeline idea can't explain.
One counter-argument states Dan remembers the first, unaltered history because he comes from a time that all people live with the first history. When he (or Livia or whoever) travels back, he travels to the time the first history is altered to create the second history. The men and women in this time, Dan's past, have no knowledge of the first history, since it has not happened (and never will happen). After completing his objective, Dan returns to the present, retaining the knowledge of the first history and, after a quick Internet search, the knowledge of the second history.