If you can play trumpet, you can also play flugelhorn. It is in the key of Bb just like the trumpet. The tubing is the same length, it is just shaped a little different. There is a reason it is shaped like it is. There are only a few inches of cylindrical tubing before it goes into the larger conical section. You cannot easily put the valve section in the part of the tubing that that is conical. Because of this, the leadpipe (called a shank on the flugelhorn) goes straight into the valve section. As soon as the tubing comes out of the valve section, it gets larger. The large amount of conical tubing gives the flugelhorn its very deep, dark sound that it is known for. It is also harder to put a tuning slide in the tapered section, so on most flubelhorns, the shank can be pulled out or pushed in to tune it. (Bach and maybe a few other manufacterers put the tuning slide in the conical section.)
Another difference is the mouthpiece. It is a lot like a cornet mouthpiece, but it has a deeper cup; also to give it a darker sound. Most manufacterers notate the flugelhorn mouthpiece with a "FL" after the number. For example 3C-FL.
Flugelhorns are usually used in jazz, gospel, and studio music, but they can also be used in other situations.