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About

MiKTeX is a widely used TeX distribution available only for Windows. For a typical (La)TeX setup, you will also need an editor, which functions as a graphical front-end to the distribution. You can find a big list of editors at our question LaTeX Editors/IDEs.

Installing

You can download MiKTeX for free. If you choose the Basic Installer, more packages will be installed when you use them for the first time; if you choose the Net Installer, it will install all packages right away. (Cf. What is the difference between the basic MiKTeX and the complete MiKTeX?)

When installing, make sure to install the TeX distribution (MiKTeX) first, and afterwards an editor. This way, the editor will most likely be able to find the TeX binaries automatically and do the configuration for you.

During the installation process, you will be asked if you want to install it as a single-user or a net installation [I'm not entirely sure if these are the specific terms used. doncherry]. Unless you know very specifically that the net installation is what you need, the single-user will be the better choice. It has nothing to do with being able to use LaTeX on several Windows user accounts, you can do that with the single-user installation as well. (Cf. Difference between administrative and user mode of MiKTeX)

Learning

If you're just beginning to learn LaTeX, The Not So Short Introduction to LaTeX2ε is a popular choice, you can find more options at What is the best book to start learning LaTeX?. Also, take a look at Best Way to Start Using LaTeX/TeX?. Besides that, you seem to have found tex.sx, so you're in the right place already :).

Alternatives

The other of the two popular TeX distributions if TeX Live. You can learn about some of the differences between the two at What are the advantages of TeX Live over MiKTeX?.

You might also come across proTeXt. This is in a category of its own in a way. It simply is a bundle of software, each of which you could get independently as well. The two most important pieces of software are MiKTeX (distribution) and TeXstudio (editor). proTeXt is a good choice for a total beginner, since it sets you up with everything you need and it includes a detailed installation guide. (Cf. What to download, proTeXt or MiKTeX?)

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