Have you made an account? That's the first step.
Then you can either browse or search for any item you want, using the "Buy" button at the top of the page to browse (Pet supplies are under Home & Garden
Hehe!). Then to bid on something you first need to read the listing thoroughly (check shipping costs, return policies, methods of payment accepted, condition of the item, and double check that it's EXACTLY what you want). Make sure the seller has good feedback (to the right hand side on every item's page it says "Meet the Seller" and shows their feedback (it should be above 90% in my opinion, and I rarely bid of it's less than 95% and with a viable reason). You can read comments from past buyers to decide if the negative feedback is something to worry about.
If you decide you want to buy the item you may have several choices. There's "Bid Now" "Buy it Now" and "Best Offer." I don't know how to do Best Offer as I haven't tried it yet. "Buy it Now" means you can purchase the item instantly for the price set by the seller (it shows "Buy it Now Price" in the listing). To bid, you have to decide what the maximum price you're willing to pay for the item is (I factor in the shipping cost and then decide), and then at the bottom of the item listing it has a box (underneath "Ready to Bid?") that says "Your maximum bid." Type in the maximum amount you're willing to pay, and Ebay will automatically bid up to that amount for you. Say it's in the last minutes and someone bids .50 cents over your max bid and you decide you want to up your bid .50 to see if you can sneak in there and get it... Then you can click "Place Bid" at the top of the page or enter a new maximum bid.
My secrets... To win you have to be watching the item when it ends. I enter my maximum bid when the auction has 1 minute to go, and then if I have time and desire I can enter one higher bid should I need to. It doesn't always work, but not everyone has figured out that to win and get a deal you have to watch as it ends, and bid at the last minute.
I pay immediately by Paypal so I get good feedback from sellers.
Also, if you win something and don't receive it within 2 weeks, report it. I spent almost $100 on a rat cage once and just kept waiting for the seller to communicate (I e-mailed several times) or the item to arrive. I waited 30 days too long and was unable to get a refund for any of it under Paypal/Ebay coverage.
You must report it within 30 days to get any kind of refund.
Also, try out the "Watch This Item" feature to put items in "My Ebay" so you can compare prices and decide which one you want. Then you can check your watched items often to remember if you have anything on Ebay you'd seen that you wanted.
Hope that helps! Feel free to ask anymore questions.