I just had some trouble setting up LaTeX on Windows 7. I think I had some of these issues in the past however when I performed this installation years ago. The following steps are in some ways more of a guide for myself in the future than anything. Obviously I am putting it online in the hopes that someone else may find it useful as well.
Download and install MiKTex. There are some options on how to do this. What I did was select the "MiKTeX 2.9 Net Installer". I had to download a file called "setup-2.9.3959.exe" which I then had to run twice. Why did I have to run it twice? Because it would only do one of two things: 1) Download the MikTex distribution onto my hard drive (compressed) or 2) install the distribution FROM a place on the hard drive.
So I had to run the setup executable once to download the distribution, and once to install it.
Important Note: When the setup asks you something like: "You can choose whether missing packages are to be installed on-the-fly: " answer "Yes". If you don't answer yes, it can create problems with integration with TeXnicCenter.
Adobe Acrobat Reader
If you don't already have it, you can get it at the reader homepage.
Ghostscript and GSview
You can download this piece of software at the TeXnicCenter homepage. I didn't have any troubles with the installation until...
When you launch TeXnicCenter for the first time, it will ask you for the location of your LaTeX files. In the case of MikTex, I found them in C:\Program Files\MiKTex 2.9\miktex\bin
You may also need to know the location of your .ps file viewer. Since I installed Ghostscript and GSview as described above, my .ps viewer was in C:\Program Files\Ghostgum\gsview\gsview32.exe
There, now you should be able to load up a .tex file in TeXnicCenter and build it and view it.