I want to install applications on a shared computer so that only I can use them. Can this be done?

The grand majority of macintosh applications don't need to be actually installed to run. Most would be perfectly happy to be double clicked from a CD.

Making matters simpler... go into your home folder and make a new folder called "Applications". You may be surprised to see it immediately take on the Applications folder icon. The OS is actually very prepared for what you are going to do.

After installing an application, it's almost certainly going to be in the /Applications folder. Open that up, and just drag and drop it into YOUR applications folder. Done. Other users do not have access to that folder in your home. They can see it's there but can't open it.

You may have problems running automatic updates on an application if you move it. You may need to move it back to the /Applications folder, run the update, and then move it back. Things like iPhoto would require that.

There are other ways of dealing with this such as setting permissions on the application etc, but really this is the easiest and least confusing. ALSO as an added bonus, time machine will back up your applications. If you have time machine to NOT back up your system files, it won't back up your /Applications folder, and if you have to restore, you will have to reinstall any apps you installed, unless they're in YOUR applications folder.