I noticed when I jacked up the rear driver side wheel that it has a bit of play in it. I pulled the wheel in and out and it moved some back and fourth. What can I do to fix this? Can I do this on my own?
The axle itself isn't to blame if you have lateral 'in and out' play. Check or replace the wheel bearing that is allowing the axle to slide in and out. If you can undertake the job successfully or not is something you can answer better than I can. If you are at all unsure about anything, get the proceedure from the workshop manual for diagnosing and replacing a rear wheel bearing and read it before beginning the job. EDIT: If you meant 'back and fourth' in relation to wheel rotation, then you have play somewhere in your dirveline. Which can be worn axle splines, worn or incorrectly adjusted differential components, play in the universal joints of the driveshaft or within the transmission itselt. Some play is expected, but if it is accompanied by clunking or drivability complaints then it will need looking at.
that linear movement is there for heat expansion. without it, your 3rd member would sound and look like a bowl of grapenuts. fords generally use a c-clip style axle as do most normal duty vehicles the c-clip holds the axle from coming out, yet wont fall out because the bevel gear shaft(also known as spider gear shaft and some call it a pinion shaft not to be confused with the main pinion shaft) keeps the axle from traveling in far enough to allow the c-clip out of its nest. now imagine taking out the play when it gets warm all that pressure has to go somewhere! so it snaps the c-clip, those chunks go straight to your bevel gears causing them to frag, and those chunks blow out your differential cover sometimes. its normal for 1 side to have a little more play than the other, since people tend to turn left more often, the drivers axle tip gets a little more wear on it.on a modern ford axle, the bearing is free floating.
Axle shaft bearing and retainer and wheel bearings are all inexpensive parts and yes this can be done at home. Look at a service manual to see what is involved. It is possible for the axle and wheel to detach from the truck so do fix the problem before driving it. see