For .dmg files [D isk iMaGe files], the Disk Copy program in your Applications/Utilites folder opens them. (sometimes the OS 9 Disk Copy will open them too, but usually not).

.sit files are opened by S tuffi IT Expander. If you find and open Stuffit Expander, it also has an iSupport menu you can use to find out about Updates.

Most of the time these files are opened automatically, but if not, find the program and then drag the file onto it.