Most desktop and laptop computers made since (at latest) 2014 are 64-bit systems, and some (2016) mobile phones and tablets are,also.
On most computers, there is usually an "about this system" icon or button in the System Settings program that can tell you.
Fedora and other GNU/Linux
Access Gnome System Settings, and click Details (usually at the bottom).
You'll see if your computer running a 32-bit or 64-bit OS next to OS Type. Just above that is your Processor type. It's possible to have a 32-bit OS on a 64-bit processor, although you may see reduced performance. The reverse is not possible.
Typically, on GNU/Linux systems, all applications will be compiled with the same word size (“-bit:ed-ness”) as the OS; at the very least, software installed through your Package Manager (eg, the program named Software) should be. It's unusual, but possible, to have a 32-bit browser on a 64-bit OS. The reverse is not possible.