Yes, Ebay allows Dropshipping and the process is simple - you just set up an auction for a item available from your drop shipper. When the item sells, you pass the customer's info unto the drop shipping company. They will then package it and ship it to your customer. They will put your company's information on the package, even including your company logo. When the product arrives, the end consumer will have no idea the merchandise came from a third party. With the need to package and ship eliminated, you'll have more time to set up auctions and market the products, thus increasing your profit potential.
When you set up your eBay auctions, you will, of course, need to make sure that the item sells for more than it will cost you, after factoring in all fees. An easy way to do this is take your cost including shipping, add 10%, and use that as the minimum bid. Charge a few bucks for shipping, and you'll be guaranteed a profit when it sells. Adding a buy-it-now option 10-20% above the minimum bid encourages people to pay a little extra to get the item they want faster.
Before listing an item, you'll want to do some research on past eBay sales and current listings to make sure no one is selling the item for cheaper. You don't want to list an item that has little chance of success, as you will still have to pay listing fees on unsuccessful auctions.
In order to become successful, you will need to establish relationships with several drop shipping companies. When you are first starting, these companies will require you pay for goods before they are shipped, so use a credit card to insure prompt delivery.
You don't want to risk a negative feedback caused by slow delivery. After you've established yourself, many companies will extend you a line of credit, allowing you to have the items shipped before you pay for them.
Starting a drop shipping eBay business, entails very little financial risk. You won't be buying any product until you have a paid order, so you won't get stuck with unwanted inventory; at worst, you'll waste some time and loose a couple bucks in fees. This is one of the few businesses you can actually start making a profit before you have any real expenses!