A field is a place on a component for player-editable text. A component can have more than one field.
A player can access a component's fields by selecting the component and hitting the "/" key. Alternatively, they can right-click the component and select Write.
Containers can be open or closed, and tiles can be up or down. Any field in one of these components must also be set to open, closed, up or down. When a player edits the fields in one of these components, they will only be able to edit the fields which match the component's current state. For example, they will only be able to edit a field set to closed when the container is closed.
You can find more information on view permissions and open / closed containers at Containers.
To add and manage fields for a component, go to edit the component and select Fields. That will give you a list of the component's fields (initially empty) which you can add to and manage.
A field's name is what the player sees as its title when they edit the field. Fields that have a state (open/closed or up/down) will be editable by players only when the component is in that state, see the section above.
Fields are defined while editing components, but the specific text of each field is a property of the individual object, not the component in general. That means there must be one or more objects on a Surface first, and then those objects' field text can be set.
One way to do this is to use the same procedure as above in "A player's view of fields" for each object. Another way is to go to edit a component and select Objects. That will give you a list of objects in use. Now you can go into each object individually and set its fields' text, or you can bulk edit (see Bulk Editing).