Sniping is the term used for bidding on an item just before the auction closes.  

For sniping to be possible the auction needs to have a fixed end time which allows the sniper to bid in the last few seconds and leaves other bidders unable to respond. eBay has fixed end times.

The primary aim when sniping is to give other bidders no chance to respond to your bid.  However, you will also not be able to bid again if you do not beat the current winners proxy so you need to bid your maximum.

Being sniped for the first time usually happens when a buyer is relatively new and usually comes as a complete surprise. Depending on the popularity of the items being sought by the buyer they may get sniped repeatedly and need to learn to do it themselves or keep being outbid.

If you wish to get involved there are three main methods.

Manually

• If you are on a dial up Internet connection which times out every few hours check that it will not be timing out when you are about to place your bid.
• Open the item you are going to snipe on in 2 browser windows
• Enter your bid into the box in the first window (ensuring that you enter the correct value)
• Press Review Bid,
• Enter your password in the box.
• Switch windows and refresh
• Keep refreshing periodically until there are only a few seconds of the auction left. About ten if you are new to sniping.
• Switch back to the first window and press the place your bid button.
• Switch back to the first window and refresh again
• You should see that your bid has been placed, if your maximum was higher then the previous winners proxy you should now see that you have won the auction and depending on how near the end of the auction you placed your bid the auction may have ended otherwise refresh again.

Sniping Web Sites 
If the auction ends at a time when you are unable to bid manually or with a programme on your PC there are web sites which will snipe for you.  Most have a basic, free, service and charge a fee for extra features like remembering lots of snipes, sniping at the very last moment, placing a number of items into a group and bidding on each one until you win one.
Use of a sniping web site involves registering with them and they will need your auction user-id and password to be able to bid on your behalf.

Sniping Software
There are programs available which will automatically snipe for you saving.