Firstly stand up, or at least sit up. Gas goes up so if you're lying down, you're less likely to burp. You then need to drink a heavily carbonated beverage, preferably with no ice. This could be any type of soda or any drink with fizz in it. By swallowing the beverage, you will necessarily introduce gas into your stomach. When the gas rises in a burp, it may bring other gases up with it, which is helpful if you're trying to relieve excess air.
After you have finished all of the drink close your mouth and nostrils so that you cannot inhale any additional air. Then exhale and swallow the exhaled air with saliva. In this case, you introduce air just so that you can burp it. This is useful for burping on command but might not help release existing gas.
You will then need to ask someone to gently pat you on the middle of your back or you can alternate with rubbing in circular motions. This can stimulate the air to rise, similar to when it's done with babies.
Close your mouth as you burp and let the gas come out through your nose. Hold your hand up to your nose so that the air released dissipates against it. Doing this will help your burp be as subtle as possible unless of course you are wanting to do this as a party trick.