Rules may vary for citizens of different countries but in general he needs a General Visit Visa and needs to provide these documents:
- a current passport or other valid travel identification
- 2 passport size colour photographs
- evidence that you can support yourself during your trip, eg bank statements or payslips for the last 6 months
- details of where you intend to stay and your travel plans - you shouldn’t pay for accommodation or travel until you get your visa
For visa's in general you need to prove you're going to leave again, you can support yourself and (maybe) that you're not going to make trouble while you're wherever you're going.
So, what do you need to do for your friend? Probably nothing but personal letter from you stating that your friend is going to stay with you and you're OK with that isn't going to hurt. If the parents are covering the income you don't need to prove that you have money, although you could mention that you'll be providing food as well as accommodation if that's true.
But really he just needs to have a clear idea of where he's staying and what he's doing. As TheMathemagician says above in the comments make sure he has a full address and contact details for you -- if immigration stop him one thing they may (actually, will probably) do is phone you and confirm the story. You writing a letter up front helps with this, but doesn't guarantee anything.
As for how the parents demonstrate they can support him, i.e. how much they need to have? There's no clear figure -- enough to cover his reasonable costs for his time there based on his plans. That figure can vary, it depends on if you plan to travel around the UK, sightsee a lot, or just try and do things on the cheap. I don't want to put a figure on it, but I hope you get the idea.
This document [PDF] has a lot more info that might help him fill in the application. But you'll see there that there are no set limits or even suggested values -- it'll all be up to the real person that reads the application to decide on it.
For what it's worth, new graduate visiting a friend in London as a gift from his parents (who will also provide spending money) does not sound like the sort of thing that would raise any flags. But you really can never tell, and it does depend where he's from.
Watch out also for any changes to the visa rules, I don't think there are any pending before summer but it's always a chance -- he'll probably need to wait until 3 months before his travel date to apply.
My quote above says you don't need booked travel and I'm pretty sure that last time I helped someone fill in a visa application you did need confirmed booked (return, or at least leaving the UK) travel. Having confirmed booked return travel never hurts, although he needs to be prepared to cope with the cancellation cost if the visa is denied.