Well, you first need to have two accounts; an ebay and a paypal one. Make sure you have access to a postal address, usitumie ya kazi- things can always be pinched by colleagues.
You can link the paypal account to a credit or debit card. Remember to be very careful with giving away your bank and card information. Look around wazua for threads on this.
Next, link the paypal account to the ebay one and you're good to go.
As Horton has said, make sure the seller ships to Kenya. For a start, I'd advise you to use only top-rated sellers and purchase small quantities of whatever you need.
Stuff normally takes 30-60 days to reach Kenya, sometimes even much longer. I believe this is because they use ships which are much slower but very cheap. If you want, you can email the seller and ask them to use a faster method (DHL, UPS etc). They will quote a figure and add this charge to the item. Make sure to ask for a tracking number and an electronic copy of the courier payment slip.
Also be sure to ask about the sellers return and refund policy. Do not buy an item if there's no guarantee of a refund in case goods are damaged or you simply dislike what you got.
Some sellers will ask you to send money to them via EFT, Western Union or Moneygram. Be careful with these kinds of transactions as you will not have any buyer protection.
When the item arrives, you may or may not be asked to visit the customs officer at the post office. This costs a hundred and something bob. If the package is deemed to contain an item thats liable for duty, you'll need to pay this at the office before they release it.
If you discover something wrong with the item, contact the seller via ebay immediately and lodge a dispute. Then send back the item and ask for replacement/ refund.