You don't have to be VAT registered; you will have to confirm that you aren't on every transaction you work on, but that's it.
IIRC, you simply sign up with your email address and a password, give them a lot of personal information, including your bank details for them to make transfers to. From then on, a few days before the gig, you give your name and email address or phone number to the pub manager to start the ball rolling, so they can create a purchase order they will eventually send you. You acknowledge that purchase order, then sign it off and send it over once you've played the gig. The pub will then sign it off and request head office to pay you.
In theory this takes 3-4 working days if the initial purchase order arrives before the gig.
Do keep in mind that Invapay takes its cut from the transaction, so always add £5 to your normal fee whenever you're paid through this system if you don't want to end up shortchanged, albeit by just a few pounds.