While it's getting very common for dropshippers to charge either an account fee upfront or a monthly fee, the great part about dropshipping, you're costs are essentially limited to your marketing. That said, if you're going to be selling on a platform like eBay then you have to be careful not to get too carried away. A big rookie mistake is that people rush in and list 100s of products because they think, well it's not costing me anything and it's increasing my chances of getting a sale, but of course the kicker comes when you get the eBay listing fee charges.
If you use that method, but don't price competitively enough to create sales volume, then those listing fees can drag you under real quick. When listing a dropshipped item, you also have to be very careful to calculate your costs. Listing costs, final sales costs, payment gateway costs, shipping costs and anything else related to the sale or again, you can end up loosing money on a sold item.
How to get started, well that comes down to research. You have to research your products, research your competitors and then research suppliers. When you've found products that you want to go with, then start listing.