Wellll, what I've done before now is to cannibalise an old rug which has been totally and utterly wrecked, and use that the mend the one that needs it, OR you could go into a charity shop and try and find something in the same sort of material as the rug which needs mending, which is as cheap and cheerful as you'll get.
Mine ripped his Rambo sweet itch rug and the local tack shop were unable/unwilling or both, to mend it, as the excuse was that Rambo wouldn't give up any material to do it!! Yes, lame excuse I know, and the result was the damn thing didn't get mended at a time when I needed it - I went to the Countrywide shop (outlets all around the country) who do rug repairs, and they did it OK. So that might be worth getting a price for if its really badly ripped and/or needs buckles or whatever replacing.
Sorry no advice on how to repair but if you need to replace the rug, I can highly recommend the weatherbeeta dura mesh fly rug. It's a tough mesh and my rug trasher hasn't managed to rip it yet.