how to stop email spam

I have been getting unsolicited e-mails (spam) sent to my
IP address. These e-mails, you don't even have to open, and it's a good thing you don't! They are headlined with dissgusting pictures.
Anyone else have this problem and what do you do about it, if in fact there is anything?
I have children that use this computer for school projects and would like to know what safeguards there are.
Cheers