By default, pictures go into the "Friends / Customer Projects" Gallery (because that's where most user-submitted pictures belong and non-admins can't change what Gallery their new picture is going into). You'll usually have to change the Gallery field from this default.
Note that you can put a picture in more than one gallery.
When you use the Picture Browse button to add the picture, PLEASE LOOK FOR IT IN THE LIBRARY FIRST! If the image file was already used in a product page or a blog post (or wherever), we don't want to keep uploading additional copies of it. You can search by filename (which can be partial) to make it easier to find out if the image file has been uploaded already.
The rest of the fields should be self-explanatory or have help text under them.
Note that you can associate Gallery Pictures with the Products used (which will put a link to the Product page under the picture) and you can optionally choose to show this picture on those Product pages as well.
Approve (or Remove) a User-Submitted Picture
You will receive an email message when a user submits a picture. They will have been informed that the picture was submitted and is awaiting approval (by a message on the site) and will also receive a copy of the email you get.
Follow the link in the email message to go to the new picture's edit form.
Check all the fields to make sure they are accurate and use the Publishing Options section at the very bottom of the Edit form to make the Gallery Picture "published". Or, you can use the Delete button if it's not appropriate.
Note that you can see the list of "submitted-but-not-approved" pictures at the bottom of the main Galleries page. (Nobody sees this except admins.)
If you need to communicate with the person who submitted the picture, you can "reply all" to the email message you received, or use the link on the "submitted-but-not-approved" pictures list.
Note that the customer will also get an email when their picture is published.