MiKTeX is an up-to-date TeX implementation for the Windows operating system. See the MiKTeX project page.
You can download MiKTeX on a Windows machine with a fast internet connection, save the downloaded files on a flash drive, and take the flash drive to a Windows computer without a fast internet connection and install it there. Follow these instructions to download the file. First, go to the MiKTeX project page, and click MiKTeX 2.9 under the download link. This takes you to the MiKTeX 2.9 download page. Scroll down to the section about "Installing a basic MiKTeX system", shown below:

Click the Download button and save the 163.89 MB "Basic MiKTeX 2.9 Installer" file wherever you like on your hard drive. Or, save it on a portable flash drive so you can take it with you wherever you want to run LaTeX. Double click the .exe file to begin installing MiKTeX. There are the usual screens about accepting agreements and where to put the files, all of which have acceptable default values. The screen below, however, is good to pay attention to, because it allows you to set the default paper size (in the US, we use letter paper, not A4 paper) and to tell MiKTeX to install missing packages from the internet without bothering you about it. If you are working on a computer that isn't always connected to the internet, you might want to select "Ask me first" instead of "Yes".

After this box and the next one, MiKTeX will start installing. It took about 5 minutes on my desktop computer.

During installation you can say that you want the default paper size to be letter (8.5 by 11 inches). But that didn't work for me on my PC. So I did Start, Programs, MiKTeX 2.9, Maintenance (Admin), Settings (Admin), giving me a window that looks like this:

Here I chose letter (letterSize). Then MiKTeX had to rebuild some format files. At least now the PDF files that are produced are 8.5 by 11 inches!
The MiKTeX project page recommends that you update the packages that come with the installation program. This is pretty easy, but I'm not sure how important it will be to a new user of LaTeX. At any rate, here is what to do. In Windows, click Start, Programs, then find the MikTeX folder, then Maintenance (Admin). Select Update (Admin). That should bring up a dialog box like this one:

These options are fine, so click Next to get something like this:

I left all the packages checked. I notice that the only one I use is hyperref, which confirms that it isn't that important to update all the packages. Even so, click Next and wait a little while for it to finish.
I wanted to install the floatflt package. I thought MiKTeX would install it automatically when I first tried to use it, but this didn't happen. So I used the MiKTeX package manager: Start, Programs, MiKTeX, Maintenance, Package Manager. It looks online and finds a list of all available packages. If you type floatflt in the Name box and then click the Filter button, it will find just that package. Click on it to select, then click the + button to install it.
