The short version is that you have to first fund your account with cash. Then you can make offers (up to 50% off of listed prices) to sellers, or you can buy for the asking price. COMC then keeps the card in your account until you request it to be shipped to you. For 1 week shipping (the cheapest), it is basically $3.50 + 25 cents per card. At the end of every month, they run a special that drops the 25 cents to 15 cents per card. There are many variations of the shipping based on timing and bulk, but that's how it generally works.
They also charge you a penny a month per card if you send them cards to sell, but I don't think they charge you to hold onto cards you purchase on COMC.
It is pretty easy to sell on, even the low-end stuff, if your prices are low enough.
It also serves as a free price guide, since they have a license with Beckett for all sports. I buy stuff from them almost every day. I flip a good bit of items on there as well.