Let’s take a look at the dotted half note (also known as a dotted minim). This note has an oval note head, a stem and a dot. The dot goes to the right of the note head in the middle, whether the stem is going up or down.
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A dotted noted is really simple to understand. A dot after a note simply increases the duration of the basic note by half of its original value. It is equivalent to writing the basic note tied to a note of half its value. There are various types of dotted notes, including dotted whole notes and dotted quarter notes. Any note can be dotted and as a result have its value increased by half its original duration.
You first of all need to know the duration of the original note. Ahalf note lasts for two beats. So how many beats would a dotted half note last for? The answer is three beats. 2 beats plus half the value of 2 beats (1 beat). 2 beats plus 1 beat equals 3 beats. It means that when you come across a dotted 1/2 note, you should count 3 beats. Hold the note for its own length, plus half of its original length.
You can think of a dotted half note as equal to the length of one half note tied to a quarter note, or as three quarter notes tied together.
In other words, a half note = 2 beats in 4/4 time. Half of that length = 1 beat. 2 beats + 1 beat = 3 beats. Count 1-2 for a half note, and 1-2-3 for a dotted 1/2 note (dotted minim). 
Dotted Half Note in 3/4 Time
Here’s the dotted 1/2 note in a 3/4 time signature. 
A 3/4 time signature means that there are 3 beats in a measure. In the first measure, there are three quarter notes. Each note lasts for one beat. In the second measure, we play the note on beat one and hold it down for three beats. Try this on your piano.
A dotted half note has the same time value as a dotted half rest. A half rest lasts for two beats while a dotted half rest lasts for 3 beats. When you come across a dotted half rest on a musical piece, it means that you shouldn’t play anything for three beats.
Much more information on musical notes and rests here.
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