Word of advice for people doing this the first time. Buy the silver body PL-259. As has already been said, solder sticks to this type the easiest. Many new comers will melt the coax before they can get solder to stick to the nickel body. The trick to soldering this correctly is all about how hot your iron is. I'd rather have 200 watts and only need to hold it on for 5 seconds then 40 watts for 60 seconds. If the coax starts to get too hot before you can solder all of the connections, just cool the connector with a damp rag.
I've also found it easier to have a small pencil iron that can fit inside the holes on the connector body. If the tip will fit and reach the braid without touching the body, you can easily get sufficient solder to connect the braid by filling the hole like this. As soon as the solder touches the body, remove the pencil and hit it with some real heat to flow it out. This way you know you bonded to the braid and didn't just fill the hole.
I've also found it easier to have a small pencil iron that can fit inside the holes on the connector body. If the tip will fit and reach the braid without touching the body, you can easily get sufficient solder to connect the braid by filling the hole like this. As soon as the solder touches the body, remove the pencil and hit it with some real heat to flow it out. This way you know you bonded to the braid and didn't just fill the hole.