A rest is written silence, and it takes up beats exactly as a note does. Every note value has a matching rest: whole rest four beats, half rest two, quarter rest one, eighth rest half a beat.
A rest does not mean "nothing here". It means "a silence of this exact length here". The note values plus the rest values in a measure have to add up to what the time signature asks for — which is also the fastest way to check you have not misread something.
A beat of sound, a beat of silence, a beat of sound, two of silence: four in all.
Rest
Length
Where it sits
Whole rest
4 beats (or a whole measure)
Hanging below the fourth line
Half rest
2 beats
Sitting on top of the third line
Quarter rest
1 beat
Zigzag across the middle lines
Eighth rest
½ beat
A single hook
The whole and half rests look almost identical; the difference is whether the block hangs under a line or sits on one. The way to remember it: the whole rest is heavier, so it falls; the half rest is lighter, so it floats.
Common questions
Which rest gets one beat?
The quarter rest, the zigzag symbol, wherever the bottom number of the time signature is 4, as in 4/4, 3/4 and 2/4. Where the beat is a different note value, the rest for that value takes the beat: in 2/2 it is the half rest.
Does a whole rest always fill a measure?
Yes. It is also the sign for a full measure of silence in any time signature, so in 3/4 it lasts three beats and in 2/4 two. Only in 4/4 does it equal exactly four beats.
Is a half rest always 2 beats?
Only when the quarter note is the beat. A half rest lasts as long as a half note, which is two quarter notes, so with an eighth-note beat, as in 4/8, it lasts four beats and fills the measure.