About 3 months ago I switched from Mouse to Trackball and have been very satisfied with it.
Cleaning is an issue with a Trackball just as it is with a regular Mouse.
Any product which has a ball in contact with your hand or a desk surface, will pick up dust through the gaps.
( Mouse users who dislike having to clean a mouse usually go for an optical mouse - something I considered but rejected in choosing my affordable Trackball T-BC21 from Logitech )
My first thoughts were to pull the red ball upwards and out, but it felt like it was held in, so I instead turned the Trackball over and spotted some screws :)
Reaching for a screwdriver is the wrong thing to do.
On the underside is a hole and all that is required is to insert something non-sharp into the hole to push the ball out until it drops into your hand.
(Poke: If you have a pencil with an eraser on the top, then use the eraser end)
If you must use a pen or other sharp object, then placing a bit of cloth over the end should prevent the sharp end from damaging the ball when pushing.
...is where most of the dust will accumulate, in particular, the area around the white dots, is where you should work hardest, as these dots are important for working the trackball smoothly.
The rectangular window...
...in the trackball holder should be dust free, and anything non-sharp (I used the corner of a piece of paper) will do the trick.
Professionals will likely suggest a cotton bud from a cleaning kit, or something similar instead of the pencil and paper I had to hand :)