When the soldering iron is ready, place its tip on the first soldered bit that doesn't have a wire connected to it.

Once the solder begins melting, add a little pressure and you will be able to find a hole through the board.

Once you can see the hole, remove the soldering iron and perform this on the rest of the lone soldered bits.

Insert your needle through the holes you just opened and wiggle it to clear them of any extra solder.

Set the soldering iron down (only on its holder) when not in use.