Plan on being in the US at least a week or so. Here's a brief rundown of the procedure.
1. Fill in the on-line application. You can do this from the UK. At the end of the application, it will prompt you to make an appointment to give your biometric data. It will tell you where to go in Chicago to do this. I believe it will also prompt you to pay the application fee as well, but I'm not 100%sure.
2. Once in the US and after the biometric data is done, you'll have a maximum of 2 weeks to get your supporting documentation to the consulate. They do not allow in-person appointments anymore, so you'll have two choices. You can apply by post or by courier. Postal applications do take a week or two. Couriers will cost a bit but you should get the visa back the same day or next day.
You can make the appointment for the biometric data before leaving the UK and arrange for a courier as well, so once that's done it should give you a bit more of an idea of how long it will take.
Try checking out
www.uk-yankee.com There is a lot of info about the UK visa application process in the US. The majority of posters on there are in the UK based on marriage and numerous experiences have been posted on there.
You will need quite a bit of documentation. Both passports, marriage certificate, bank statements, evidence of savings or job offers, proof that you can support yourselves without needing public funds and evidence of accommodation.
