The natural minor scale, harmonic minor scale and melodic minor scale may at first seem complicated to understand. However, they are actually very easy to comprehend if you can see their relation to the major scale. Before reading on, if you do not know how to read music comfortably, I would first suggest reading this article to get the basics.
Natural Minor Scale
If you begin the major scale on the 6th degree, and play all notes of the scale from there to an octave higher, you create the natural minor scale. The example below explains this. First, we have the C major scale. If we start this scale on its 6th degree (note A) and play to the next A (an octave higher), we create the A natural minor scale.
Notice that the notes of the A natural minor scale are the same as the notes of the C major scale. Therefore, these two keys are relative to each other. That is, C major is the relative major of A minor and A minor is the relative minor of C Major. In addition, notice that both these keys have the same key signature: no sharps and no flats.
Harmonic Minor Scale
The seventh note (leading note) of the minor scale is often sharpened in a piece of music in a minor key. This creates a stronger resolution to the key note (tonic). The scale which demonstrates this is the harmonic minor scale. Below is the harmonic minor scale in A. Notice the F to G# interval. This interval is an Augmented Second.
The augmented second has a distinctive character. It is not often used in western melody. Because of this, the melodic minor scale was devised. Below is the melodic minor scale in A played ascending (going up in pitch). Notice that the sixth and seventh degrees are raised. This creates a strong pull from G# to A without the augmented second.
Melodic Minor Scale 
Below is the melodic minor scale in A played descending (going down in pitch). Notice that the raised 6th and 7th that were played ascending are cancelled when playing the scale descending. In other words, the melodic scale descending is exactly played like the natural minor scale.
Below is the complete melodic minor scale in A:
Let’s look at another example of these 3 minor scales.
Natural Minor Scale in E
Below is the G major scale. If we start this scale on its 6th degree (note E) and play to the next E (an octave higher), we create the natural minor scale in E. 
Notice that the notes of the natural minor scale in E are the same as the notes of the G major scale. Therefore, these two keys are relative to each other. That is, G major is the relative major of E minor and E minor is the relative minor of G Major. In addition, notice that both these keys have the same key signature: the F# note.
Harmonic Minor Scale in E
Below is the harmonic minor scale in E. Notice the 7th degree of the scale was raised from D to D#.
Melodic Minor Scale in E
Below is the melodic minor scale in E played ascending. Notice the sixth and seventh degrees are raised:
The melodic minor scale in E is shown below played descending. Notice again that the 6th and 7th degrees of the scale are no longer raised when the scale is played descending (exactly like the natural minor scale in E):
Below is the complete melodic minor scale in E: