To delete music from itunes hightlight the track (or tracks) you want to get rid of and hit delete on your keyboard, itunes will thow up a box asking if you want to move the track to the recylce bin or just remove the track from the library (or if you've hit delete by accident there is a cancel button).
For the ipod either plug it into a PC that doesn't have itunes on it and format it as FAT32 or in itunes go to edit > preferances > ipod there you can select the playlists that copy on to the ipod (ipod must be connected to access the ipod tab).
Above is based on itunes for windows, hopefully its the same for the Mac if thats what you're using