To run a non-executable sh script, use:
sh myscript
To run a non-executable bash script, use:
bash myscript
To start an executable (which is any file with executable permission); you just specify it by its path:
/foo/bar
/bin/bar
./bar
To make a script executable, give it the necessary permission:
chmod +x bar
./bar
When a file is executable, the kernel is responsible for figuring out how to execute it. For non-binaries, this is done by looking at the first line of the file. It should contain a hashbang: