In written music, notes have two properties: pitch and duration or their note values. Pitch is indicated by the note's location on the staff. Duration however is slightly more complicated. Notes have different appearances to indicate their 'note values.' There are whole notes, half notes, quarter notes, eighth notes, sixteenth notes, 32nd notes, and so on.
We usually only work with notes values down to 16th notes because values beyond that are rarely used in most music.
These note values are relative depending on the time signature. In a time signature of 3/4, a quarter note gets one beat, but in 3/2, a half note gets one beat. If this seems confusing, don't worry about it. You can still count out 2 beats for each half note and it will work out; you just have to play it twice as fast. :-)
Eventually in reading music, you will run into dotted notes. These dots are called augmentation dots because they make the note longer. The dots give the value of time-and-a-half. This means you take the length of the note and add half of it. So if you have a whole note (4 beats) with a dot, it would be a whole note plus a half note (4+2) for a total of 6 beats. If you have a dotted quarter note, you'd have a quarter note plus an eighth note (1 + 1/2) for a total of one and a half beats.