How do I make my own Minecraft Server with Bukkit?

Are you looking to use a recommended build or developer build? Either one will work, but the recommended build has been tested and recommended for use by the public while the developer builds can be a little more on the unstable side.

What do I do if I run into some problems?

There are plenty of ways to seek help with your problem. The first way is to check the troubleshooting pages on this website. The second way is to look around on Google to see if other people have encountered your problem, and if they have, see how they dealt with it. Finally, the last way you can try to resolve your problem is by going to the Bukkit forums and making a topic.