Most Mac applications are packaged as DMG files. Double click these to mount them as a drive icon on the desktop, then go into that drive. You can then drag the application straight into your Applications folder, then eject the drive icon.
StuffIt is used to unpack SIT files. If you double click on a SIT file to unpack it, it should open the file up in StuffIt. If it asks you to select a program, just choose StuffIt from your Applications folder.