Disagreeing with the other answers, there’s a common convention to use a .sh extension for shell scripts — but it’s not a useful convention. It’s better not to use an extension at all. The advantage of being able tell that foo.sh is a shell script because of its name is minimal, and you pay for it with a loss of flexibility.
To make a bash script executable, it needs to have a shebang line at the top:
#!/bin/bash
and use the chmod +x command so that the system recognizes it as an executable file. It then needs to be installed in one of the directories listed in your $PATH. If the script is called foo, you can then execute it from a shell prompt by typing foo. Or if it’s in the current directory (common for temporary scripts), you can type ./foo.
Neither the shell nor the operating system pays any attention to the extension part of the file name. It’s just part of the name. And by not giving it a special extension, you ensure that anyone (either a user or another script) that uses it doesn’t have to care how it was implemented, whether it’s a shell script (sh, bash, csh, or whatever), a Perl, Python, or Awk script, or a binary executable. The system is specifically designed so that either an interpreted script or a binary executable can be invoked without knowing or caring how it’s implemented.
UNIX-like systems started out with a purely textual command-line interface. GUIs like KDE and Gnome were added later. In a GUI desktop system, you can typically run a program (again, whether it’s a script or a binary executable) by, for example, double-clicking on an icon that refers to it. Typically this discards any output the program might print and doesn’t let you pass command-line arguments; it’s much less flexible than running it from a shell prompt. But for some programs (mostly GUI clients) it can be more convenient.
Shell scripting is best learned from the command line, not from a GUI.
(Some tools do pay attention to file extensions. For example, compilers typically use the extension to determine the language the code is written in: .c for C, .cpp for c++, etc. This convention doesn’t apply to executable files.)
Keep in mind that UNIX (and UNIX-like systems) are not Windows. MS Windows generally uses a file’s extension to determine how to open/execute it. Binary executables need to have a .exe extension. If you have a UNIX-like shell installed under Windows, you can configure Windows to recognize a .sh extension as a shell script, and use the shell to open it; Windows doesn’t have the #! convention.