Having admin rights means being able to create or change ACLs, see HelpOnAccessControlLists.
For a personal homepage
Check if there is a HomepageTemplate with prepared ACL lines or some other already-configured configuration settings.
It is important to ensure your homepage is easily readable and writeable so it can be used as an open form of communication by everyone.
The easiest way to create personal (or private) subpages for your homepage is to use the MyPages action.
Alternatively you can also do it manually, using the HomepageReadWritePageTemplate, HomepageReadPageTemplate or HomepagePrivatePageTemplate. They usually have some prepared ACL line on them, e.g.:
#acl @ME@/ReadWriteGroup:read,write @ME@/ReadGroup:read
That @ME@ in the template will be expanded to your name when saving, so those 2 subpages (YourName/ReadWriteGroup and YourName/ReadGroup) of your homepage will be used for allowing read/write or read-only access.
Now you only have to maintain those two subpages (based on HomepageGroupsTemplate) of your homepage (maybe they even have been auto-created for you) and put the people on them for allowing them access.
For a project page
See if there is some <ProjectName>Template with a prepared ACL line for your project pages and use it for creating new subpages.
Use <ProjectName>/ReadWriteGroup and <ProjectName>/ReadGroup etc. as you would do for a homepage (see above).
AutoAdmin configuration and administration
Add this to your wiki's configuration file:
# indent the line below like your other settings: from MoinMoin.security.autoadmin import SecurityPolicy
Create an ?AutoAdminGroup page. It is usually a good idea to create an empty page for this.
That page (and also other group pages used with autoadmin, see below) should be ACL protected with write access limited to allowed people. They are used as source for some ACL information and thus should be treated like the ACLs they get fed into.
Enabling a home page for AutoAdmin
Just add the user name (same as home page name) to the AutoAdminGroup page. Alternatively, if you want to enable this feature for all users of some specific group, add the group page name to AutoAdminGroup.
All users directly or indirectly on AutoAdminGroup will get admin rights on their own homepage or subpages of it.
This is needed for the MyPages action, but can also get used for manual ACL changes.
You also can define some page templates with pre-made ACLs for them to use for new homepages or subpages of it.
Enabling another (project) page for AutoAdmin
Add <PageName>/AdminGroup to AutoAdminGroup.
Also create that <PageName>/AdminGroup group definition page and add at least one user or one group to that page, giving them admin rights on <PageName> or subpages of it.