Google have updated the procedure for how to add a new user to Google Analytics yet again. This is the December 2013 version.
How to add a new user to Google Analytics
Log into Google Analytics.
Click the Admin button at the top right of your dashboard
Select your domain
You may have more than one domain on this account.
Select the domain that you want to add the new user to from the drop down menu on the left of the dashboard.
Then click on User Management. It's the second option down.
This will bring up a dashboard on the right hand side.
At the top is a list of the existing users for Google Analytics on that website.
Add a new user to Google Analytics for your website
Go to the section underneath the list marked Add Permissions.
It has a text box below it.
Enter the email address of the new user that you want to add.
Check the box that says you want them to be notified by email that you have added them.
Choose the level of involvement you want them to have. Read and Analyse is the basic level. But there is the option for more hands on management.
The new address join the list that contains your email address on the dashboard above the Add Permissions section.
Delete A New User/Admin From Google Analytics
You also have the option to delete any user.
Look to the right of any one of these email addresses. You will see the word delete.