9 times out of 10 the old bearings are shot (rusty, ball with a flat spot, too much slop, etc.) so it's not worth screwing with. Just buy the whole rebuild kit (roller shafts and bearings) from Bob Roberts and be done with it.
For the few times the bearings are still in good shape but just gunked up, soak them in mineral spirits for about 15 minutes (work the bearings by hand to loosen things up). Now blow out the bearing with a can of air until dry. Then oil it with two drops of 3 in 1 oil and reassemble the trackball unit.