First, you will need to register your lamp (See Registering Your Friendship Lamp for a walkthrough) and then create or accept a group (See Setting Up Groups and Inviting a Loved One for more info). If your Friendship Lamps were ordered as a set, your group will already exist on your dashboard after the lamp is registered to your account.
Once these 2 steps are completed, you will be able to customize your Friendship Lamp!
Click on update or remove each item you want to customize:
Here is a video where you can see how to customize your lamp: