I was printing with my Anet A8 and it pulled the filament spool off of the shelf I have the printer on and forced the filament out of the extruder. I took apart the extruder and removed the debris that was left inside, re-leveled the bed and tried to start another print. When the extruder tries to feed the filament it makes a clicking sound and won't extrude. How do I fix this?
There are a number of unanswered questions which may serve as a guideline to narrow down a solution.
Instead of attempting a new print, consider to remove the filament again. Shine a light from below and look into the barrel of the extruder to determine if you can see light. If this is mechanically impractical, move to next option.
Manually feed the filament into the extruder. Use the panel to advance the filament rather than creating a print. Does the filament feed properly?
If yes, the problem is not in the extruder system, nor the heat block or hot end. You said you re-leveled the bed. Double check that the nozzle is not being blocked by the bed, preventing filament from extruding.
If the filament does not feed properly, you may not have completely cleared the heat break, hot end, or nozzle. If you can get or have nylon filament in the correct size, perform a nylon cleaning operation. This involves removing the existing filament, raising the nozzle temperature to 240°C while pushing nylon through. You have to be able to manually force the filament through until you see only clean nylon from the nozzle.
I have had to push nylon in at the correct temperature, then pull it back out without any extrusion due to the depth of the blockage.
After you've pushed as much as you can to get clean nylon (or none), cool the hot end to descend below 140°C. After a moment or two, set the temperature to 140°C and forcibly remove the filament from the upper portion of your assembly. It may require pliers and substantial force to get this out.
Repeat the heating, extrusion (or attempts), removal until you get clean nylon from the nozzle and clean nylon at the tip of the removed filament.
Only just today, I had to clear my nozzle using this method, but I was unable to get a reasonable extrusion of clean nylon. I have a 0.4 mm nozzle drill and applied that to the tip of the nozzle, carefully.
I found a burned on segment by this additional step and succeeding nylon cleanings went well and my nozzle is printing cleanly again.
If you don't have nylon, you can perform similar cleanings (called cold pulls) with ABS or PLA.