If you are looking to have more than 1 profile on your xbox 360 then you will need to do the following:
To access Xbox Live on another account (i.e. you want more than 1 profile on your xbox 360), then you will need to create a new Hotmail email address.
To access Live in full you will need an xbox live gold membership subscription, this will apply for each additional account so if you want 3 different profiles (if the console is shared by different family members for example) then you will need 3 different gold memberships, one for each.
Xbox Live Silver is free, but you cannot play online multiplayer, send voice messages, participate in video chat, for these you will need a Gold subscription.
To save costs you would be best to share a gold membership on one account for playing online and then each other user having a silver account for general playing, or share one online account between all users, athough this may not be ideal.