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contact band's agent (or, if band don't have an agent, directly i guess)
prepare to be ignored probably
you'll probably be asked to "make an offer"
in theory, you'd work out how much you can pay = (expected number of tickets sold - cost of venue - cost of promotion - any extra costs such as riders and maybe hotels) and make that offer
probably it'll be end up being too high
nobody will show up despite your best efforts
go home, cry, eat pasta for a month to make rent

as cynical as this sounds, though, sometimes amazing opportunities will come up and you'll get to put on a sold-out show for one of your favourite bands. it's a bit like seeing your favourite band, except you'll make back a small amount of the money you've lost on the proceeding dozen shows AND you'll likely get to go drinking with them afterwards. and that's the BEST.

The key question in terms of the process is whether the band have a booking agent. (Most bands who do will say on their website or Facebook page or wherever and give those details to contact for gigs). If they do, whether you get them is likely to depend on whatever the strategy is for the band and it might prove to not be possible, or they might charge a lot of money.

If they've not got an agent, contact the band directly via an email or FB message and offer them a gig. No need to be too detailed but it's good to sound enthusiastic and show some knowledge of the band so they know you're not just a promoter approaching bands at random but really do want to put them on.

They may come back to you and say yes or no outright, they may come back to you and ask for money upfront or they may come back to you and say you need to go through a manager of whatever (in which case you repeat the same process in an email to the manager).

Great though it is to put on bands you love, if you want to run nights in the long-run you have to treat it like a business (unless you have money you can afford to do). Be fair to the bands in terms of covering their expenses out of profits but also be realistic about what you can afford to pay them and how many people they're likely to pull in. I've known bands (luckily not ones I've booked) charge £250 and only bring 3 people and that can be a bugger if it's your money you're losing. Be prepared to say no if the money doesn't add up.

Similarly work out your costings and margins - i..e how much it'll cost to cover the cost of venue hire and bands and how much you'll need to charge/how many people you'll need to not lose money and make sure you stick closely to that...

done it for a few years in reading. it's not rocket science. get a room. get a pa/soundperson. get some bands. tell people about it. tell people about it again. make sure kit share is sorted. tell people about it again. try and get all the bands time to soundcheck.

i'd suggest that you start off by doing a gig with just your friend's bands (or friends of friends) to figure out the rough process before booking the beatles.

communication and not being a dickhead are key. run a tight ship. get some friends to help out.