Sometimes, in spite of all your efforts, things don't go right. Headers might end up crooked, or you may accidentally solder to the bottom of the board when you should have soldered to the top, or vice versa.
Getting headers back off again can be difficult, but it's not impossible. You'll need a few tools and a lot of patience, but it's most definitely do-able - once, at least. If you get them on wrong a second time it's very likely the copper pads will be damaged or the pins will get bent beyond repair, so take your time and double check before you solder all the pins.
It's much easier to fix a mistake if you've only soldered the end or corner pins down, so do a test-assembly of your project before you commit fully.
For headers that are on crooked, it can sometimes help to use the side of your soldering iron to heat all the pins at once, then gently nudge the header so it straightens out while the solder is soft. Be gentle - you can damage your board or break the headers if you push too hard.
To un-solder just one or two pins, you can use solder wick. Solder wick is a braided copper strand that comes in a coil. If you place it next to your solder joint and melt the solder with your soldering iron, the molten solder will soak away from your electronic components and into the wick.
The wick will get saturated with solder, so be sure to move to a clean spot each time you use it.
For more intense jobs (like removing fully soldered headers), upgrade to a solder sucker. This little sucker will vacuum up molten solder and leave your pins and board clean.
Depress the plunger, then heat up your solder joint until it's molten. Place the head of the solder sucker over the molten pin and press the button. The plunger pops up, sucking the solder with it. Voila! Repeat on all the pins and your headers can be wiggled loose and reattached.