Instructions
Think of a theme that relates to the types of games you play or your favorite hobby. Obvious Gamertags such as "MasterChief123" will most likely not be available.
Add a clan tag to the front of the Gamertag if you're part of a clan. Clans are groups of people that play games for fun and competitively. They demonstrate this by displaying an abbreviation of their clan name in front of their Gamertag (e.g, [TPF]MyGamerTag).
Use symbols and numbers in the Gamertag. Doing so increases the odds of the Gamertag being available. Gamertags are limited to 15 characters total.