Your path is just where your shell (the shell is the program that launches all the other programs, a bit like double clicking in windows on a file icon to start a program in windows) looks for programs to run.
at the command line to see what it includes.
To compile mpeg2encode, download the source file to a temporary directory (yopu might want to make a directory for compiled packages)
tar -zxf mpeg2vidcodec_v12.tar.gz
then change into the newly created sub-directory, and for this program, you only have to type
in the new directory (the one with files like README).
After a minute (if you have an old computer like me) the computer will stop spouting stuff and you can look in (I think) the subdirectory src/mpeg2enc and there should be a file called mpeg2encode.
Copy this to one of the places listed under your path.
If it does not exist already, you might want to create your own bin directory in your home directory or maybe use /usr/local/bin to give everyone access.
/usr/bin and /bin are generally used for system executables.
/opt/bin (if you have it) is often used for precompiled binary packages you may have purchased.
I suggest, on balance, that you put it in /usr/local/bin if you have root access.
The program should compile setting mpeg2encode to world executable so yes everyone can run it.