Wait 'til right after a rain or water the area first. If you have weeds, the moisture will help the weed killer cling to the broad leaves of the weeds.
Additionally, it's a good idea to use gloves if you're going to spread by hand. While, as frank says, it's not toxic, it sure dries your hands out and can irritate any small cuts you might have.
Wait for a few days to mow the lawn, but don't collect the clippings or rake it. The cut ends of the grass (and weeds) will fall to the earth under the grass and keep it moist as well as help spread the fertilizer...
Wait a few weeks and then re-treat the lawn as above...
Good luck!