For a one-handed knot that doesn't require relacing, try the one-handed variant of the "Ian Knot" from Ian's shoelace site. The result is identical to a standard shoelace knot, though I suspect it will take some practice to master.
A more straightforward option is the "one handed shoelace knot" Unfortunately this one does require relacing, but allows for a very simple one-handed knot once the lace is set up. The idea is that you "anchor" one end of the lace permanently, letting you tie off the other end by looping it back on itself. A diagram is probably more useful than my attempted explanation:
The linked page has step-by-step instructions with diagrams, details, and a photograph of the knot in use.
If you have a lot of eyelets and don't mind a slightly loose fit, there is also a one-handed lacing which relies on eyelet friction alone to keep the lace tight -- you just tuck in the loose end of the shoelace rather than tying it off.
(I found the link to the anchored one-handed knot in an answer by Rajath, which was swiftly deleted for being a link-only answer. However, it seemed to me to be the best suggestion posted so far, so I thought it worth salvaging.)