Joining meshes

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My game problem is more complex than this as it involves joining meshes with more verticies together, but simplifying it :

If I have 2 squares (4 verticies each) and I want to join the right hand side of the first square, to the left hand side of the second square so there's now one mesh (made of 2 squares joined together).

ie. join

.-. and .-. to become .-.-.
| | | | | | |
.-. .-. .-.-.

Is there an easy way to do this? Particularly is there a clever way that will eliminate the extra 2 verticies (ie. two individual squares = 8 verticies, 2 together = 6 verticies)