Index -> Interface -> Campaigns
The campaigns are several connected series of single player missions, each with special objectives. When you access the campaigns, you will see a series of navigation buttons.
Load Game allows you to resume a previously save campaign scenario, while Campaigns begins a new one. When you click Campaigns, a menu of options will appear.
The Tutorial Campaign is designed to teach you the Star Chamber interface and the basic rules of the game. If you're new to Star Chamber, these tutorials are a great way to get started.
The other options present scenarios in which you play a key role in the unfolding story of the Republic. Selecting a campaign will lead to another menu where you select the specific mission you wish to undertake.
Note that the difficulty setting for campaign missions can be adjusted using the dropdown menu at the upper left of this screen. The four levels, from least to most challenging, are Ensign, Lieutenant, Captain, and Admiral.
For more information, see Playing a Campaign Mission.