Well, it depends how close
to the speed of light you get. You can't actually travel at
the speed of light (except science fictionally, of course, where you can travel as fast as you'd like, hyperdrive/warp drive/etc. being fairly common).
If you're adhering to Einsteinian relativity, though, then the time dilation equation -- for constant
speed -- is, well, easier than trying to do formulas here, check out the section on "Time dilation due to relative velocity" in wikipedia
Bear in mind that your traveler may also be under acceleration the whole time... (for example, you could provide your traveler with 1g of constant gravity, which would make life comfortable, accelerating at 1g half way, then decelerating at 1g to slow down)... which really complicates the math. See the section on "Time dilation at constant acceleration" in that same article. I worked it out one time and wrote a little Linux script for myself since it isn't pretty.