You haven't heard this from me, but I often just make a big blob of solder that covers all pins on one side of an IC such as the one in the video above. Use flux liberally, you'll clean it later. Then - while the solder is liquid, of course - I lift that IC side up, just off the board. I use some sharp, thin tool like the tip of an Xacto blade under the chip to help lift it. Once one side is free, I do the other.
If you have a big chip with many pins and you know you won't put it back in, you can just cut the pins off with an Xacto, as close to the chip as possible, and remove the chip body. You can then easily desolder the pins one by one, or a few at once.
For 2-terminal parts like resistors and caps, you can also try the blob method, but ideally you'd want two irons simultaneously: one on each side, and just lift the part with the irons like they're tweezers. They do make tweezer-type iron tips for some more serious irons, but few DIY folks have those.
There are also small hot air tools for desoldering, but I don't use them enough to give advice on them.