Back in the old days of eBay, getting payment for the item was entirely left up to sellers: you had to choose your payment service, sign up for it and then send links to your buyers. Now, though, eBay handle most of the complexities of payment for you with their checkout.
How Do I Offer the Checkout?
The checkout will be offered to your buyers automatically. When they win an item, eBay send them an email with a Pay Now button that takes them to the checkout, and they can also access it through their My eBay page.
It is in step 4 of the Sell Your Item process, the payment and shipping step, that you can choose which kinds of payment you want to accept through the checkout and which you dont.
PayPal: You should be accepting PayPal. You might want to click Edit Preferences, however, to either select or de-select the tell buyers I prefer PayPal payments box you dont want to tell people you love PayPal when you only tolerate it. If youre selling Buy it Now items, you can also tick the box to require immediate PayPal payment for them.
Money orders and cheques: tick these boxes if you want to accept the more traditional payment methods. Your address...