First of all take a long run up at it, and secure your supply lines for Valium and/or wine.
Well, ok, humour aside, there is a lot involved, and I thought I'd expand a previous posting into a bit more of a Rainbow guide in getting started.
You have to know why you want to exhibit and if you're doing it as part of a group, that you're all on board and involved. You might all decide to work to a theme, or do your own thing, but either way you need some kind of cohesion and commitment, eg you don't want to agree to make new work for the exhibition, and then find that someone drops out because they have left it all to the last minute and have nothing to show. You need to plan carefully and sort out whatever it is you want to do, before you apply for places.
It can be a long process of course, so everyone needs to be prepared to keep going over a long period, and stay together. Typically, publicly funded galleries have a long lead in time, and often plan exhibitions 2/3 years in advance.
Having established that you're either going solo, or you're doing it as part of a group, and what your planning to exhibit by way of a theme or style, then you need to look for a suitable venue.
You need to be clear when writing to people in galleries that you know what your doing and what you're offering. A good way to do this is to make an exhibition pack with a Proposal, that contains all your contact details, what you're planning on showing (ie number of quilts/paintings) and how much linear wall space that will use up. Include lots of lovely photos. Will anything need plinths or special arrangements? Can you provide the battening, and hanging if necessary? Will the work be for sale? Will it be part of a tour and will postage be payable or are you delivering? If international artists are involved, have you sorted out customs? Are there any charges for your services or for the work itself? Will there be items for sale in the shops? It's easier, if it's a Council for example, for one of you to be a creditor on the Council's systems, and all payments would go through that one person. Are you registered for VAT or do you need to be?
Try to think of it from their point of view - why would they want to choose you from the hundreds of applicants they undoubtedly have?
There are many ways you can help persuade a gallery that you are serious. You could offer to help sort out the funding - many publicly funded galleries rely on Arts Council grants - and have to apply for money to support your exhibition. You could arrange postage to and from, offer workshops, childrens activities, studio mock ups, catalogue production, opening events, advertising, and willingness to attend meetings to discuss, no matter where they are. Most importantly you have to have an exhibition that is of a high standard and is of interest to, and fits in with, the gallery's other plans.
Do not be disheartened if you don't get a response to your enquiry. Many galleries get so many offers that they don't reply. Keep trying though. You will find somewhere.