On eBay the seller of the item that you are purchasing needs to accept your payment method in order to proceed with the deal. Most eCommerce sellers accept PayPal because it transfers funds immediately and the seller can ship your item right away instead of waiting for funds to clear. Therefore you can easily create your self a free PayPal account for your self and there will be no issues.

But if you do not wish to open PayPal account, you can try out the following payment options,

Bill Me Later
Credit cards and debit cards
Skrill
Paymate
ProPay
Pay upon pickup
Escrow
Other payment methods

Source: http://pages.ebay.com/help/pay/methods.html

There are a number of ways to pay on eBay. Most sellers offer more than one option. Some payment options offer more protection than others, so be sure to select a method of payment that makes you feel comfortable.

If you have additional questions about payment options, you can contact the seller directly. You can find the seller's email address by clicking on the User ID in the listing or by looking in the End of Listing email that you received when the listing closed.

Sellers may not ask or require you to pay by instant cash wire transfer services such as Western Union or MoneyGram. They may not ask you to pay by cash. These payment methods are not permitted on eBay. Please refer to the Accepted Payments policy for details on permitted and non-permitted payment methods. Payment services that are not permitted on eBay may, in fact, be outstanding services for consumers in other contexts. eBay’s evaluation relates only to whether a particular service is appropriate for the eBay Marketplace. If a seller asks you to pay with a payment method that is not permitted on eBay, report the seller.

Clicking the Pay Now button is the fastest way to pay on eBay. Common payment methods available using the Pay Now button include:

• PayPal
  
• Credit Card
  
• Personal checks, cashier's checks, or money orders
  

• PayPal
  
• Credit Card
  
• Personal or Cashier's Checks
  
• Money Orders
  
• Escrow
  
• Bank to Bank Wire Transfer