Familiarize yourself with the common rest symbols. A whole rest is a small black bar that hangs from the second to top line on the staff; a half rest is a small black bar that lays on the third line of the staff; a quarter rest is a symbol that resembles the number 3 (if it were written using calligraphy); an eighth rest is a thin line with a hook; further subdivisions of the beat are marked by adding more hooks (a sixteenth note has two hooks and a 30-second note has three hooks).
Read the time signature on the piece of music you are attempting to play. This will tell you the amount of beats a measure of music has (the top number) and which type of note gets the beat (the bottom number). While the length of most rests are based off of subdivisions of 4/4 time no matter what the actual meter of the song is, whole-note rests tend to mean a whole measure of silence in any time signature.
Examine the written music paying special attention to any rests. These rests are counted the same as their note counterparts. A half-rest takes up two beats like a half-note; there are two eighth rests in a quarter rest just as there are two eighth notes in a quarter note. Tap your foot and count along with each measure until you are comfortable counting the rests.
Practice this piece of music until you can play it confidently (including the rests). Start slowly and build up speed as you get to know the song better. This is easiest to do if you can locate a professional recording of the piece of music you are attempting to play. That way you can actually compare your playing to professional quality playing, which will help you know if you are counting a rest wrong.