Do you need a special soldering iron?

I don´t think so. Use appropriate tip. Maybe a solder-sucker to clean things up a bit before resoldering the new parts.

If only replacing with same value/higher quality, no schematics should be necessary.

Be careful and pay attention(!) to what you are doing (not reversing the polarity of caps - if that is being replaced etc.).

Moderate use of hot-glue. If any.

Best,
Mike

Biggest danger to circuit boards is too much heat. You want an iron 20-30 watts with a small tip. Be sure it's well tinned and you're using rosin core (not acid core) solder. 60/40 lead tin mix is what you want.

Second biggest danger is making cold solder joints. If you're not experienced, practice on some scrap wire. Don't use too much solder - you can easily created unintended bridges between adjacent circuit board traces.

You'll want the solder sucker to help remove the old parts - beware of applying too much heat to the board during this process or you may cause the foil to lift from the board.

I don't think you'll need the glue gun.

Be sure to observe polarity markings (if any) on capacitors. Not all have them, but installing an electrolytic cap backwards will get you some nice fireworks.

You can buy a roll of solder sucking wire at Rat Shack that works fine.

I agree with Ghost, would be very careful with a soldering gun around a PCB (printed circuit board).