Buying online is simple and easy. Most online retailers and auction sites require you have an account, so you'll have to set that up first. They usually have as well a list of FFL transfer agents near you and the cost of the fees they charge. Find the transfer agent that you want to use and make contact with them and either get a copy of their FFL or see if the will fax it to the person you are buying from. Some online gunshops like Bud's might have a copy on file already so you won't have to go through that step.
Once you get your accounts set up and choose your FFL transfer agent you go shopping.
This guy happens to have five 7mm RM in stock, if you chose to do so you would use the "buy it now" button to purchase it. Once you purchase it, you contact the seller and finalze the purchase details. Then you contact your FFL who will receive the rifle and handle the transfer, you let him know what is being shipped and from whom. If necessary this is when they'll fax the copy of their FFL to the seller.
Once the seller receives payment and a copy of the receiving FFL, they should provide you with a tracking number on the shipment. Then when your agent receives the rifle you go in and fill out the paperwork, pay the FFL fees, and hopefully walk out the door in less than an hour with your new rifle (unless you have a waiting period). Just like buying and selling anything else online except you have to use a third party if the rifle crosses state lines.
Just make sure to only buy from people who have a good track record. If the seller is unknown make sure the offer an three day or more inspection period and a full refund minus shipping at a minimum when buying used. Check closely the shipping costs which should never exceed $35 IMO, as I've shipped several and even with packaging materials and insurance I rarely exceed $30.