Once you have the fiancee visa, the hard part is over! As was said before, you don't need a COA, just the fiancee visa. Your fiance can make a tentative booking with the registrar for the date you want to get married and after you have that, you have to register your intent at a register office designated to handle marriages between foreign nationals and British citizens.
Simply find the website for the county council in which your fiance lives and phone up the nearest one explaining that you want to register your intent to marry and that you are a foreign national. From that they should be able to guide you to the correct registry office where you can give your notice, usually a minimum of around 17 days before the wedding. You both must be present as you will have to answer simple questions about yourselves and each other (just names, birthdays, etc). After this, your notice goes up on a board and after it's been up for two weeks or so, you are good to go for either marrying at a register office or other council approved location of your choice! Things are a bit different if you want to get married at a church, but unfortunately I can't offer much advice on that as we were married in a hotel.
