Legato playing is done with a techniques that involves hammer ons and pull offs. Hammer on means playing a note and then pressing the other note with your next finger without using the plectrum.
If you have a finger on on the the third fret and first fret and you play the note on third fret. After doing this, when you lift your finger, you will also hear the sound of the first note. This is called pull offs. This method is used by lot of guitarists so that they can play fast.
You can try this on a scale pattern, especially the Major Scale
You will find out what you are playing sounds good and your right hand doesn't have to do lot of work.
I will post an exercise about legato playing soon.