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 ReadWritePageTemplate, ReadPageTemplate or PrivatePageTemplate. 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 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).