The flute really isn't a woodwind anymore, and is normally made of metal now. It produces very bright and joyful notes.
The piccolo is the smaller relative of the flute. It is exactly the same in all respects -- notes and fingerings -- but is a lot smaller than the flute and it has a higher pitch.
The clarinet is a single reed instrument. It plays a wide range of music from classical to jazz. It also has a very wide range of notes that can be played.
The oboe looks very similiar to the clarinet except for the fact that it has a double reed. The oboe is widely used in classical compositions.
The saxophone is a single reed instrument. Depending on the player it can sound mellow or strong. It does everything from pop to big band to jazz but also has its place in classical music.
The bassoon is a double reed instrument. Because of its size, it plays very low notes and is often the backbone of the orchestra.