Using ICs from old computer hardware and such
The best way to desolder chips is with a hot air station.  However, unless you already have one, the cost will be way way more than any savings from salvaging old parts.  Hot air stations are also the best way to hand solder modern fine pitch parts, so that can be a legitimate reason to get one, then also use it to salvage old parts.

The reason a hot air station is good for this is because it can heat all the leads simultaneously.  Once the solder melts, you just pick up the part with tweezers.