Use your soldering iron to heat up a through-hole on the circuit board.

Use a desoldering pump to suck up any solder residue from the through-hole.

To clear out through-holes, heat it from one side and use the desoldering pump to suck through the hole from the other side.

You can also use solder wick instead to remove the residual solder.

Repeat this for all through-holes and both sides of the circuit board.