Here’s a tip for anyone who has never studied with a metronome before: turn it on and just try to play a note on the beat with the metronome. You can also start by counting along (aloud or in your mind) or by clapping, stamping on the floor or walking along. The purpose of this exercise is to get to know how regular a metronome is and to learn to take over a tempo the metronome is indicating. It is rather useless to try and play many notes if you do not know if you can play along just one note.
Are you succeeding in playing along your note with the metronome? Try changing the tempo (faster or slower) and do the same exercise. On changing the tempo: start by putting up two or three beats at a time, you will not notice a great difference which will gradually make you faster. For a challenge: put the metronome of very different tempos and try being in rhythm with it from the moment you start playing (preparation is the key: make sure you count along before you start playing!).
Some people might find these exercises simple, others will find it hard to keep up the steady beat. Just keep in mind: it might be difficult to play along at a faster speed because of technical limitations. Always check your technique, this might be the cause of your inability to keep a steady rhythm.
When you can play along at different speeds try changing it up a play along a scale, one note with each beat of the metronome. This can also give you technical problems, so check if your technique is correct before you blame the metronome.
Once you can play along with the beats you can start playing between de beats. Start out in a slow pace and play two notes on every metronome beat (one on the beat, the other in between the beat). You can start out by playing the same note again, and make it more difficult by changing to a scale or an exercise. Once you can do this, start increasing the tempo.
Next step is to play 3 or 4 notes on every beat…can you keep that up in a regular tempo?
It gets even harder if you assign yourself to only playing notes between the beats of the metronome. Try to divide the beats in two (as if playing two notes per beat) and then only play the note that doesn’t go on the beat. Can you keep this up? Try doing the same thing with three notes of which you only play the last two (or even harder: only play the last of the three notes).
Once you can play single notes you can try out doing short repeating exercises with the metronome. Scales will work too. Keep in mind that you do not want any exercises that give problems with technique: the point is learning to study with a metronome, not expanding you technique.
When you can do all this you will have a way to test your agility. Can you get your scales those two clicks (beats) faster?