Install jack posts underneath the floor joists next to the wall you are removing if you determine that it is a load-bearing wall. If it is an exterior wall, there is a greater chance that it is load bearing. Place a jack post vertically so it extends from the basement floor to the underside of a joist; turn the screw on the jack post with an adjustable wrench until it is firmly wedged between the floor and the joist. If you have a limited number of jack posts, you can place a wooden beam under the joist, then remove the jack post to use on the next joist.
Break the mortar joints between the cinder blocks by hitting them with a sledgehammer. Start with light taps and increase the force only as much as is necessary to loosen the blocks. Disassembling the wall in this way decreases the risk of smashing the blocks and leaves them whole for reuse in another job.
Loosen all the blocks in the top course of the wall and remove them. Placing them directly into a wheelbarrow for removal will require less work than knocking them onto the floor and having to pick them up again.
Continue removing courses of blocks until you have reached the floor and the wall is gone. Clean up scattered mortar and debris with a broom.