That's a difficult question to answer. Mainly because there really is no cheap method of shipping a cabinet due to the dimensions and heavy weight. I'm actually an employee at UPS, so please take my advice concerning this because I see music equipment come through on a daily basis:
The first thing you should know is that - assuming it's a 4x12 cabinet - it's going to be what UPS (or FedEx or whoever) refers to as an "irregular" package, meaning it is either 70 lbs or heavier and/or its dimensions are too wide/tall for the standard conveyor belts that they use for everyday packages. In this case it's probably going to be both, and those two factors are going to jack the price up on shipping.
Secondly, when it comes to irregular packages, they aren't the easiest boxes to move. So with that being said, you run the risk of shipping personnel not asking for help in the process of getting the box to where it needs to go and trying to move it by themselves. I'll leave this part to your imagination as to their various methods of transportation. This is why it's very, VERY important that the cabinet is packaged EXTREMELY well; put as much packaging material as possible in between the cabinet and the box in order to keep it stationary. You don't want a cabinet shifting around in a box! The molded, styrofoam inserts that come in guitar, amp, cabinet, etc. boxes are perfect as they limit movement within the box and keep the item itself away from the boxes' edges so that if the box takes a spill or happens upon the corner of a wall or something sharp, the contents inside are safe.
If you're the one that's shipping and it's through some sort of eBay auction or Craigslist, I would take it to a UPS store, let them do what they need to do in terms of packaging it themselves (unless you have the materials to do so, although those size boxes are very hard to come by) and give the buyer an estimate.
I shipped a cabinet a few years ago and did not follow this procedure and it cost me; the package was damaged upon delivery and the buyer demanded a refund (and rightfully so, I might add). So now I'm happy to give this advice to anyone who doesn't want to suffer the same fate!