First thing to note: there is no "Windows Live Mail 2013": the latest version of Microsoft's free email program is Windows Live Mail 2012, available for Vista, Windows 7 / 8 / 8.1 . Note that Windows Live Mail can also be installed, and runs fine, on Windows 10! (Windows 10 does come with a built-in email program, but it's very basic.) This tutorial explains the free download and installation - screenshots were taken on Windows 7, but the process is the same for all supported version of Windows. You can't download Windows Live Mail alone, but we'll show you how to customize the setup to include only the programs you want (versus all the Windows Live apps).
Note: you can download Windows Live Mail even if it's already installed on your PC. That will ensure that you have the latest version available. See the end of this tutorial to make Windows Updates automatically download new versions of Windows Live Mail and other apps as they become available.
No need to worry about 32-bit vs. 64-bit versions of Windows: as long as you are not running Windows XP, you'll be able to install Windows Live Mail 2012. Any recent computer should be fine (in doubt, see "Windows Live Mail system requirements").
Go to the official download page on Microsoft's website. To get the standard version of Windows Live Essentials, English by default, click on the big "Download now" button. For one of the other 64 supported languages, click on "Other download options" and take your pick: the rest of the process is identical.
Tip: you can either save the download to your desktop, or choose to "Run" it: it is so small (about 1.2 megabytes) that it makes no difference. The installer will download the files needed based on the programs you choose to install (which also means that you can only install Windows Live Mail while online).
Once it has finished downloading, double-click on the installer to launch it: it will ask for the administrator's password, and this is normal. It needs "elevated privileges" to install and configure the Windows Live apps you want to have. To install everything, click "Install all of Windows Live Essentials"; to install Windows Live Mail only and/or select other programs, click "Choose the programs you want to install" instead: 
Check each app you want installed; if you already have a previous version of Windows Live Essentials on your computer, the old apps will automatically be selected for update.
Click on the "Install" button to proceed: a progress bar will start its animation. The time it takes depends on the number of apps you choose, and your internet connection speed: each of the one you selected is currently being downloaded from Microsoft's servers. You can click on "View Details" to get a completion percentage and see which program downloads / installs at the moment: 
Caution: while there is a Cancel button, let the installer completely finish. Depending on the apps previously installed, canceling the installation could cause issues - the whole process typically takes less than 10 minutes.
When the setup is complete, click "Restart Later" and close all the programs currently running: shut down and reboot your computer, and you'll be able to use all the apps you just installed! (And bookmark this tutorial so you can come back to it later :) 
By default, Windows Update will only download and install critical updates, but you can configure it to include Windows Live applications in its updates. Click on the start menu, type "Windows Update", and hit Enter. Next to "Find out more about free software from Microsoft Update
", click on the "Click here for details" link. Then, click "Yes, tell me about new software (recommended)" in the dialog that opened: 
From now on, Microsoft will also check for new versions of your Windows Live apps whenever you run Windows Update (and when it automatically runs itself).
