How to open a program on linux?

In general, if you install a package that contains programs that you can usefully run without arguments, the package will add menu entries in the GUI. This isn't a mathematical certainty, but packages in Debian and Mint are supposed to do this.

If you want to list all the executable programs that a package contains, you can use the dpkg command, specifically its -L (--listfiles) option. dpkg is the command that manipulates installed packages; apt commands are about packages that are available in the distribution. To see just executables intended to be used by ordinary users, list files under /bin and /usr/bin. (See the Filesystem Hierarchy Standard for an explanation of the directories where Linux stores files.)

dpkg -L tor | egrep '^(/usr)?/bin/' 

To also see commands that are generally only useful for system administrators (and thus are only in root's PATH), include sbin directories as well:

dpkg -L tor | egrep '^(/usr)?/sbin/' 

In the case of tor, there's a system service, so you probably don't need to run any command. After installation, the next step is to configure your browser or other software to use Tor.

According to where are apt-get files stored?, the file is in /var/cache/apt/archives/

For further reading:

• AptGet/Howto
• apt-get(8)

In the original question, OP omitted the verb install from the command, which someone added in an edit. However, OP said downloaded, which would be done using

sudo apt-get download tor 

For clarification:

• Difference between apt-get -d install & apt-get download
• How do I use apt-get to only download packages?