1. Google SafeSearch. This is very easy to set up. You need to get into settings for search. It doesn't always appear exactly the same so I can't give precise instructions.
But this is the Google help page for it and should get you there:
The second big improvement in terms if Internet safety (and this is a change that affects all access, not just searches) is use of OpenDNS services (free, unless you decide to get the enhanced service).
OpenDNS is really great because it prevents even inadvertent access (like Politicalmom described), or deliberate, for that matter to any website on the lists for objectionable content (the lists can be customized extremely easily -- for example, you can restrict social media sites, video sharing, political, etc., or not). In addition to classes of sites, you can list individual ones to block or not.
This is a bit more involved to set up, but not bad at all. It really does work. If, for some reason, you need to defeat the protection temporarily you can, as administrator. I rarely, if ever, have to do that, now that I have my blocking list customized.
Most people are comfortable setting up OpenDNS, but if you are not comfortable making any kind of change to your network settings you should have another trusted person set this up for you. But you will need to be the adminsitrator with the OpenDNS password ultimately.
Good luck and I hope these work for you!