There are currently three methods of buying M&B:Esellerate
Esellerate is an online retailer, and is the site linked to from the buy button. The method is fairly standard. You will first need to enter your details and card information. When the payment is processed, you will be taken to an online reciept which shows you the serial number there and then. A copy is also emailed to the address you specified. You can request a copy of this email at any time, which can be useful if you lose your key.
There have been problems where entering the details has returned to the same page. In this case, the payment will not have went through. Should this occur, check the page for any error messages first (i.e. a missing field which is required or similar). If there are no errors, then it is likely the server simply timed out while you were trying to connect. Trying again should work fine. Esellerate's system has protection against double orders - if it picks up you made an order recently from the same email address, it will ask you to confirm.Paypal
To order through paypal, follow the instructions given on the Taleworlds website. Log into your Paypal account, click send money (make sure there is enough money in the account, or have your card details handy) and enter the address given on this website. Paypal orders need to be processed manually, so the time between ordering and recieving your serial key will vary depending on how busy Armagan and co are, though they do try to process them as quickly as possible.
In general, it is best to give the team three days to process the order. If you haven't heard anything by then, you can try emailing or sending a PM to Armagan. Be aware however than the time just after a new version release is usually the busiest, and it may take a little longer to process orders recieved during these periods.Gamer's Gate
Mount and Blade is also carried on the Gamer's Gate download service - Here