How does Genieo get on my computer when I did not download it?

It disguises into other software, the same way as Trojans do. That's why you should always choose Custom Setup when you install something downloaded from the Internet: you can have full control of what components are installed and refuse to install crap components which are otherwise silently installed in background, when you choose Standard or Express Setup.  Here for more details:http://savvygeektips.blogspot.com/2014/01/internet-toolbars-big-hassle-or-plus.html To get rid of it, reset your browser to its default settings. You should also scan your system by using ClamXav for Mac or Sophos Antivirus for Mac. I tend to prefer the former, as it uses fewer resources (see here:http://savvygeektips.blogspot.com/2013/11/clamxav-review.html) , but Sophos is a very decent product as well.

Might have accidentally been installed along with something you meant to install. It happens sometimes when you're installing a program from the internet. Just go to the control panel and uninstall it.

Genieo Search is a browser hijacker, which is promoted via other free downloads, and once installed it will change your browser homepage and default search engine http://tosearch.genieo.com.

Search.genieo.com page is found to replace users’ default homepage like Google or bing. This browser hijacker is generally brought by some malware or hacked sites with malicious codes, or it can be spread via spam mail or freeware bundling. You may know about it and the way to get rid of it here http://pcproblemsolve.com/get-rid-of-genieo-homepage-hijacking-search-genieo-com-removal-steps/

This http://guides.uufix.com/information-about-potentially-unwanted-programs-pups-infographic/ may be bundled with other software you downloaded and installed from the web. Sometimes visiting malicious websites may also lead to such PUPs getting installed on the PC. Anyway, be cautious online.