It is quite easy actually. Some big blog sites are blogger.com and xanga.com
As far as setting up the site, the above mentioned will walk you through it.
As for actually blogging... you just start writing as if you are writing a journal. I would be careful whatever you do that you do not include any personal information. If you are going to make this public, as in absolutely anyone can view it, you want to be fairly anonymous.
Unfortunately there ARE crazy people out there. You want to protect you and your family from some psycho who may want to do you or your kids harm. It's sad we have to warn against these things... but stalkers, kidnappers, identity theft theives... they don't need much to go on. So, NO last names, no actual birthdates, try to avoid mentioning the city where you live, and if you can just avoid using real names at all that's better. I have a private blog on xanga, meaning I decide who sees it and who doesn't. But even there I don't use any of our real names. I typically refer to my daughter by her mamma given nickname... buppy. ;-)
If you're careful about it all, blogging is actually quite fun. I've met some great people through blogging.