Use vibrato in your playing to add some extra flavor to notes that last a little longer than the other notes of a particular phrase. By dressing up these slightly longer notes, your playing will sound better and be more interesting.
By the way, there is more than one method of applying vibrato to your guitar playing...
Different Guitar Vibrato Methods
You can apply vibrato in a couple of different ways on the guitar. You can move your finger back and forth in a direction with the length of the neck. You can also do the vibrato movement back and forth in the direction of the frets themselves. Sometimes people call it a violin or classical type of vibrato.
The vibrato movement is somewhat difficult to explain with words so a good way to learn to do vibrato on the guitar is to watch other guitarists and copy their method. As soon as you can, watch the vibrato of blues guitarist BB King - he puts his entire hand and wrist into the move and he gets a beautiful vibrato sound. He has a pivot point that remains in contact with the guitar neck as he applies his delicious vibrato action.
How Much Vibrato Should I Use?
One of the most important aspects of vibrato to consider is when to use it in your playing - vibrato should be used judiciously - that is it should be applied at just the right time, and held on for just the right duration - And you don't ever want to have too much of a good thing. You don't want to over do or over use the vibrato. It should be thought of more as a spice to add flavor to your playing. Usually you'll want to spice up your playing by adding vibrato to the notes that last longer than the others.
In addition to the methods mentioned above, another common way to add vibrato to your playing is by using a guitar with a whammy bar / tremolo arm - this device will give you loads of vibrato with the added benefit like allowing an easy way to add vibrato to entire chords - even across all six strings at once.
A quick word of caution about the whammy bar if you're shopping for a guitar you should be aware that a lot of guitars get pulled out of tune to various degrees after using the whammy bar - Floyd Rose is the best - your mileage will vary from guitar to guitar. So if you're shopping for a guitar with a whammy bar and you plan on using it a lot, be sure to fully test out the model you plan to be and see that it stays in tune so you don't get a surprise.