A whole note in common time lasts four beats, or an entire bar of music. There is only one whole note per bar, so this is the easiest place to begin. A metronome is a good idea when you ware working on counting rhythms. Set the metronome at 60 beats per minute. It's a steady pace, not too fast, but fast enough to keep you working. Tap your foot on the first metronome click and hold the count four beats. This is an entire bar. When you reach the fourth beat of your count, tap your foot on the next beat. This will be the first beat of the next bar. The process is the same. Do this several times until you feel comfortable with whole notes.
Repeat the exercise for whole notes--only this time, you will tap your foot on beat one and hold it for two counts, then tap on beat two and hold it for two counts. You will be tapping your foot only two times per bar of music. This is because you can fit two half notes into the same space as you can fit one whole note.
Four quarter note beats will fit into the space that one whole note or two half notes fit into. Keep your metronome set at 60 beats per minute and tap your foot on every click of the metronome. When you're comfortable with this, write out several bars of rhythm. You can purchase blank staff paper from a music store, make it yourself or just use plain paper. Use various combinations of whole, half and quarter notes to create a rhythm sheet; then practice the sheet with your metronome. This not only keeps you working on counting rhythm, but it gets you familiar with writing the notes as well, which will help with your reading ability.
Keep your metronome at 60 beats per minute and tap your foot on each beat for a couple of bars. These are the quarter note rhythms you're already familiar with. Once you have a solid rhythm down, tap your foot two times on every click of the metronome, but only count one time. If you prefer, you can use the word "and" on the second tap. These are eighth note rhythms. You can fit two eighth notes into every quarter note, or eight of them into a bar of music in 4/4 (common) time.
Read as many rhythm sheets as you can. You can find rhythm sheet exercises at music stores, in practice books, or you can use rhythm exercises available on the Internet, free of charge (see Resources). After you've practiced your rhythm sheets at 60 beats per minute, set your metronome up to between 70 and 80 beats per minute. At this point, you should be using your instrument of choice to play the rhythms as you read them.