Installing Wildfly is just a matter of unzipping the distribution into your local machine. Wildfly can be dowloaded from its official website.
Once it is unzipped go in to bin directory of installation and run
standalone.sh for Linux systems or
standalone.bat for Windows systems to start your WildFly instance in default configurations. Once you see something like
13:16:12,503 INFO [org.jboss.as] (Controller Boot Thread) WFLYSRV0025: WildFly Full 10.1.0.Final (WildFly Core 2.2.0.Final) started in 18909ms - Started 331 of 577 services (393 services are lazy, passive or on-demand)
then your brand new WildFly instance waiting to welcome you at : http://localhost:8080/
Some Linux distributions, such as Fedora, have Wildfly on its repositories and can be installed via YUM/DNF:
dnf install wildfly. This, however, is not really recommended, as it tends to use slightly different versions of the libraries than the official distribution, which might cause problems that are hard to diagnose/fix.