Where a rootkit comes from
Rootkits can be installed in many ways, including through commercial security products and seemingly safe, third-party application extensions. Rootkits can't spread by themselves, but instead are one component of blended threats.
How to recognize a rootkit
Detecting rootkit-like behavior can be tedious work. When searching your system memory, monitor all ingress points for invoked processes, keeping track of imported library calls (from DLLs) that may be hooked or redirected to other functions. If you want to be sure there is no rootkit on your PC, you can use a PC scanner (e.g., the free Avast antivirus & anti-malware tools).