barcelona chair  

You might not be able to.
Since 1996, Knoll Barcelonas have had a signature stamped into the frame. If your chair has that signature, it's almost certainly Knoll.
If it doesn't have the signature, you can identify a poor copy by getting a good look at the real thing (preferably in person, but clear photos of indisputably authentic chairs could work if that's your only option) and then comparing.
It's a knockoff if it doesn't have the right number of straps (9 on the seat, 8 on the back) or the right number of tufted squares (5x4 on each cushion), or if the cushions don't hang over the edge of the frame, or the straps don't attach the right way or the frame-ends are ground wrong or the welds aren't smooth enough, or if its measurements are substantially different from the Knoll chair.
Unfortunately, though, that only works for the really bad knockoffs. There are others that are so similar to Knoll that your non-expert eye won't see any differences.
So... Don't pay more than the cost of the lowest-priced decent replica ($700 or so) for any chair represented as pre-1996 Knoll unless you can first get it authenticated by an expert. And if it's important to you that the chair be Knoll, don't buy at all unless it has the signature or has been authenticated by your expert.
http://www.knoll.com/products/product.jsp?prod_id=577

Question on bottom chair?
I have a chair like the one at the bottom of your post (different legs/cushions with the wood accent piece). Is this another style of an authentic Barcelona chair or is it being used as an example of a knock-off? Either way any info you might have on this chair would be greatly appreciated.

WKLynn
The chair in the bottom photo is a knockoff. The authentic chairs always look substantially identical to the chair in the top photo.
Don't be too disappointed, though. The authentic chairs are remarkably uncomfortable.

Thank you for the fast response.
That's what I thought. I saw your post and figured I should confirm it. I have not been able to find any other info on this chair.