By default subscribed accounts can create 8 characters, while silver accounts can create 4. There are two ways to increase your limit:
1) Daybreak Store
2) Loyalty Tokens
Each one of these can increase your maximum character slots by 3, for a total of 6 additional slots. This means subscribed accounts can reach a maximum of 14 character slots, and Silver accounts can reach a maximum of 10.
There are some legacy methods that allowed even more character slots (Station All Access and Legends server), but these are no longer offered.
Daybreak Store
Open the Daybreak Store and go to All Items -> Services -> Slots. Here you’ll find an option to buy either 1 character slot at a time, or buy all 3 at once. Buying all 3 at once is a better value overall.
Buying 3 = 2000 DBC (1800 with +10% Discount if subscribed)
Buying 1 = 800 DBC (720 with +10% Discount if subscribed)
These may go on sale occasionally.
Loyalty Tokens
In Plane of Knowledge there is a vendor named Alerynril the Loyal. This vendor only shows up if House of Thule is released on your server. If House of Thule is not released on your server, then you can log on a live vendor to interact with her.
She sells the item