First, here's the MiKTeX FAQ on this:
http://www.miktex.org/faq/basics.html
A TeX/LaTeX .tex file a plain-text file, which can be composed in any editor [even Notepad!].
Certainly, some editors are nicer than others... and some editors have features that are useful for composing TeX/LaTeX.
The program to run (on the command line) is called "latex":
(If you don't use the LaTeX package, you can use the more primitive "tex" command.) The output of "tex" or "latex" is a .dvi file, which can be viewed with "yap" on MikTeX, which can be started by double-clicking on myfile.dvi .
When ready to distribute to a wide audience, you probably want to run, for example, "dvips" or "dvipdf".
The output is a postscript .ps or acrobat .pdf file.
These commands (except for "yap") are standard for practically any properly-configured LaTeX distribution... on any platform.
Some text editors allow these "command line programs" to be invoked from within the editor. TeXShell happens to be one such editor, which also has some useful TeX/LaTeX features (like the symbol buttons and the highlighting). However, I have my own favorite general-purpose editors [which support highlighting and many other features] which I prefer to use.
For a beginner, a properly-configured-for-MikTeX editor, like TeXShell, is certainly useful. A more sophisticated editor is TeXnic, as mentioned in the above URL.