Purchase a book about reading music that you can reference as you practice time and rhythm in music. This is an ongoing process, and having a book handy as you learn will be helpful. You can find the same information online at no charge.
Set a metronome at around 60 beats per minute. This will help you keep in time as you try different rhythms. Start with a whole note, which lasts for four counts. Snap your fingers on the first beat and count to four. This is a whole note. Do this four times, always snapping your finger on the count of one and holding it for two, three, four. When you're comfortable with whole notes, try a half note. A half note lasts for two beats. Snap your fingers on one, hold for the count of two, snap your fingers on three, and hold for the count of four.
Add quarter notes to the mix. Start with a half note, snap your finger on the count of one, hold it for the count of two, then snap your finger on the count of three and the count of four. Combining the notes is what makes rhythm in music. Try this exercise until you're comfortable combining half notes and quarter notes.
Practice eighth notes next. Start counting one, two, three, four. You can fit two eighth notes in the space of one quarter note. Try a quarter note and eighth note pattern while counting from one to four. On the count of one snap your fingers (that's a quarter note, on the count of two snap your fingers twice (two eighth notes), on three snap your fingers once, and on four snap them twice. This is a pattern of quarter note, eighth notes, quarter note, eighth notes.
Combine everything. Mix whole notes, half notes, quarter notes, and eighth notes randomly. You'll notice the change in rhythm as you vary the order of the note values. The better you get at counting the rhythms, the faster you can make your metronome. The rhythms will never change, but the speed with which you snap your fingers will.