One thing i forgot to mention (that's crucial) is - good tweezers. Can't do a thing without them.
With good ones (angled, sharp, with properly closing jaws, so not bent, dulled or otherwise deformed) it's a piece of cake - you keep the part in place with them, you get a little bit of solder on the tip (not too much) and just swipe along the legs, or touch the "joint" between the component and the pad if there are no legs. If there's too much solder or you've bridged two legs, you work on the other side first, then use the wick to remove some solder and reheat just a bit to reflow afterwards.
For packages with lots of legs, you can often do all in one fell swoop - by doing drag-soldering. Then just mop up with the wick again and you're done.
https://www.youtube.com/watch?v=wUyetZ5RtPs
