Generically, user programs that come with the distro are installed in /bin, /usr/bin, or /usr/X11/bin.
Applications that are built from source or that are not packaged with the distro typically get installed in /usr/local/bin. Typically, there is some type of README or INSTALL document that explains where the application will get installed by default unless you customize the installation.
Some applications add their own file location to the PATH
From a command terminal window, you can type echo $PATH
and it will show what path that user has set.