I second this. Technically speaking, you can put the mod on your server and client and it should work (assuming you have correctly put all @SideOnly annotations as well to prevent the mod from referencing nonexistent classes.) If all your mod does is add simple blocks and items, it should work fine. In most cases, if your mod works in single player (since it actually runs an internal server), it'll work in multiplayer too.
So if you want the question fully answered, you have to tell us what your mod does.
I agree with this. If it is a more complicated mod, however, you may need to pass packets back and forth between client and server, and it would be easier to make separate mods for singleplayer and multiplayer.