In the above exercise you have a mix of quarter, eighth and sixteenth notes.
Tune your metronome to 50 BPM. Clap your hands with the metronome pulse. After you get and feel the pulse, count ta, ta-te, and ta-fa-te-fe in the right places.
When you feel conent with this tempo, increase the BPM just a little, and try again.
Practice this exercise in various tempos, and you will feel the differences between quarter, the eighth and the sixteenth notes.
This was only one exercise, but it gives you an idea how to practice rhythm with a metronome. In the future we will have many more rhythm exercises, so stay tuned.