This article will explain in detail how to add values to a picklist field that has already been created. If you haven't created the field yet, please follow the appropriate link to learn how to do so: Add Custom Fields to an Item, Add Custom Fields to a Change or Quality, Add Custom Fields to a Project.
1. Go to Setup
2. Select Object Manager
3. Locate the Object containing the picklist field
4. Select Fields & Relationships
5. Click on the name of the field to be modified
6. Scroll dow to Values and select New
7. You also have the options to Reorder and Replace the picklist values