Agreed with dog cat mom. I groom my rabbits BEFORE their weekly run. It may seem contradictory, but that means the wool I harvest is clean. When they are done running, then I pick out the big pieces of leaves, twigs, etc. before they go back in the cage, and Iet them take care of the rest themselves. By next week, they are nice and clean again. Almost nothing to pick out while spinning.
I just grab a small handful of wool ( called a cloud ) and start drafting/spinning. You can card the fiber before hand, but I think that since the fiber has very small scales and doesn't 'grab' itself as well as sheep, its harder to spin when its all well aligned.