When visiting an enabled market, open the contacts menu and speak with the USL Concierge. Speaking with the Concierge is also how you complete contracts.
After you receive your license, you can gain access to the USL Contract Board. Starting contracts are small, and are barely profitable. However, by completing more contracts and raising your USL rating, larger contracts and rewards will be available. Tooltips explaining the contract types are shown by hovering over the contract tabs.
Freight Contracts: These standard contracts are available to all captains. While not always the most lucrative contracts, combining several close-by contracts can be profitable. Contract size will increase along with your USL rating, and the number of available contracts is based on the market size and your USL rating.
Parcel Contracts: Upon reaching a USL liability rating of 20, and having a 'USL Parcel Sorting Cargo Hold' installed on at least 1 ship, these contracts become available. Only one of these missions can be in progress at a time, and the quantity of the contract can be adjusted using the red and green buttons below the contract list. Failing one of these missions can severely hurt your USL rating. Also be careful not to lose any of your parcel cargo, as this will also result in a contract failure.
Logistics: Completing USL contracts results in USL Supply and Fuel Points, which can be used to purchase supplies and fuel at heavily discounted prices at any USL station.
The configuration menu can also be accessed by clicking the 'C' button to the top-right of the Contract Board. Be careful to not have any contracts in progress when changing settings.