Once a party has been created, click the menu button to the left of the party name (box with three horizontal lines). Select "Manage Approvals", then select the "Consultants" tab. To invite a consultant, you will need to type their username in the field under the heading "Invite Consultants". Their POP username is the username they use to log into POP and it is case sensitive (never ask for or give your POP login password). Click 'send invitation', and your part is done. You will see the username of your invited friend in the list of Pending Consultants.
Once you send the invite, the other consultant will have to accept the invite before they can add their inventory to the party. They accept by going to the Parties screen and clicking the "Join" button next to the name of your party. Their name will move to the Approved Consultants column in your approvals screen. The consultant's inventory can now be added via their Manage Inventory page.
Ninja Knowledge: Be sure to communicate with everyone loading into your party about the attribute you used to create albums for the party. If all participating consultants do not have that same (case sensitive) attribute and equivalent values, your party will be difficult to shop.