I got like a 1/2" pipe from the plumbing section in Lowes, which was threaded on the end, a big ol' washer (maybe 2" wide?), and a cap to thread on the end to hold the washer. Carefully insert into tube making sure to not push the dirt in, scrape crud out, repeat. Once you get most of it out, suck up any more loose debris with a shop vac.
Once you get it cleaned out fairly well, you can Get a pvc pipe and cut it in half to get a "u" shape. Then you can actually cut it to the length you need and then just leave it in the housing and use it to provide a clean path to slide the shaft back in on. It will also serve the same purpose when you remove it the next time.
I actually didn't cut mine in half though cause I didn't feel like it. Just left the whole pipe in there. Just made sure it was a large enough diameter to not interfere with the shaft.
Some people cut them in half though, but I haven't had any problems with leaving it in there whole.
Also, I've heard of people using a tape measure to slide the shaft in on... I tried that the last time I had another axle apart and it didn't work too well for me though.