You can edit and delete your custom fields on the Contacts -> Contact Fields page.

Editing

To edit the field, click on the 3 dot iconon the right then click Edit Field. You can change the name, type, or publicity of the field here. After making all the necessary changes, click Save.

Deletion

To delete a field, click on the 3 dot icon then click Delete. Then click Delete in the confirmation dialog box. After that, the selected field will be removed from the list of fields.

See also:
Creating Custom Field