Creativity
Many people subscribe to the Xbox Live service making it most likely that the obvious Gamertags have already been taken. A good Gamertag spawns from your own creativity or is based off a hobby, general interest or combination of things. To increase the odds of Gamertag availability, add numbers and spaces.
Requirements
A Gamertag must be unique, is limited to 15 characters and cannot contain any profanity or blatant sexual content. These requirements, particularly the character limit, may make it difficult to come up with a good Gamertag. A simple way to work around the character limitation is to abbreviate longer words or use numbers when applicable. For example, try substituting "for" with "4" to reduce the amount of characters being used.
Clan Tags
As you play multiplayer games via Xbox Live you'll notice many Gamertags that have short abbreviations in front of a shorter name or in brackets. These players are associated with clans or communities, a group of players who play together regularly. If you're part of a clan this makes selecting a Gamertag easier as a Gamertag starting with clan initials is less likely to be in use.
Suggested Gamertag
During Gamertag creation the Xbox can automatically generate a a list of available Gamertags based off your first or last name. Although you may not like the suggested Gamertag they are best used to give you ideas for Gamertags if you don't mind them being something as simple as JohnS4972.