Installation is easy. Just unpack the tarball and run the install script provided. To run the utility, just do the following:
rkhunter -c --createlogfile
Essentially, the utility has two main functions. One is to look for rootkits (logically) on the system. The other is to check binaries and other files for evidence of tampering and vulnerabilities. It will even inform you about bad practices. For example, if it finds that your SSH configuration file allows root logins, it will warn you. It will also track down suspicious looking dot files and tell you about those.
The tool is interactive, meaning that by default, you need to push enter after the phases of checking are completed. However, you can run it from a cron job and disable this interactive mode.
The best way to approach using this is to install it and use it directly after a clean install of the entire operating system. Then use it periodically. It's a good idea to run it right before you update your system after security alerts. When you run it subsequently, you should be on the alert for false positive, as rootkit hunter makes hash checks of your binaries. A systems update could theoretically set off an alert as the checksums on the binaries should change.