Hello,
configuring access for non-administrators to do administrative tasks, like add member to groups, change user data an so on, needs a lot of things.
Mainly this is a 2-step process:
1. Give permission to UI elements (and possibly create new element)
2. Give permission to the approp. objects in portal (incl. custom UI elements like own Navigation Bar Resources for ex.)
3. Eventually modify UIs by using RCDCs
You have to implement or change MPRs to do such things, in addition to show some of the default UI elements you can modify UsageKeywords (Navigation, Homepage, SearchScope) values.
Best is to start with the following documentation:
https://technet.microsoft.com/en-us/library/ff393653%28v=ws.10%29.aspx
https://technet.microsoft.com/en-us/library/ee534913%28v=ws.10%29.aspx
https://technet.microsoft.com/en-us/library/jj134312%28v=ws.10%29.aspx