[SiriusHardware]

How deep are your pockets?

At the bottom of the pile is the humble manual desolder pump which has a cylindrical metal body, a spring loaded plunger at the top end, a tapered teflon nozzle at the bottom end and a trigger button on the body. You melt the solder joint with your soldering iron and then while the solder is 'wet' whisk away the iron, apply the tip of the button to the still molten solder and press the button. They are cheap but crude and you usually have to do each pin several times until you get it reasonably clear.

Next level up from that is something very similar to the above but in place of the teflon tip it has an electrically heated hollow metal nozzle which you place over the pin / pad, allow the solder to melt and then press the button.

Far better than either of these is a proper desolder station which incorporates an electric pump which provides constant suction through the hollow metal tip. As you might guess these are a lot more expensive, in fact until quite recently a complete desoldering gun station from a 'respectable' manufacturer like Weller would set you back quite a few hundred pounds. Nowadays I would expect you could get something functionally equivalent from China for in the mid tens of pounds upwards - however I have no experience with these so I'll invite everyone else to chip in with their recommendations.

As well as all of the above there is something called 'desolder wick' or 'desolder braid' which is flat copper braid soaked with flux. You can press this onto a soldered area with the flat tip of a soldering iron and it will soak up quite a lot of solder. It's not a substitute for any of the above but there are certain jobs where a bit of desolder braid will work better than a desoldering iron, so really you need a desolder pump / desolder iron and some desoldering braid in your desoldering armoury.