Desktop devices
Microsoft Windows:
Try key combinations such as:
Windows Button and Pause Button OR

Windows Button and R. In the window that opens, type “msinfo32”

You can also find your system architecture here next to "System type". Just look for the number 64 or 32.
Apple Mac OS:
First click on the black Apple symbol and then “About This Mac” (pane).
Mobile devices
Android
Depending on your individual device and Android version, this can vary a lot. Here’s an example on how to find it on a Samsung Galaxy S 4:
Open “Settings”
Tap on "Options" tab
Scroll down to device information
Look for the information under “Android Version”
Most likely, the steps are similar on your phone/tablet. In any case, look for areas such as: Settings, Options, About Phone, Software Info…
iOS
Different versions may vary a bit. Here is how it works on iOS 8.2:
Open “Settings”
Press “General”
Press “About”
Look for the information under “Version”