Do Any Laws or Rules Restrict What I Can Say?
The internet is largely self-regulated, which means there are few laws. Also, laws vary greatly from country to country.
Unless you're doing something quite unusual, you don't even need to think about the law. You can basically write whatever you like.
Obviously, all the normal laws of your country also apply to blogging. Don't deal in counterfeit or illegal digital or real-life goods. Don't promote any illegal activity.
Don't steal others' work. Google works out who copied who, and will only show the original work. Quoting parts of a print or online article, in order to comment or critique it, is fine.
If you use someone's full name, and write bad things about them, they'll almost certainly find your blog and take action.
Criticism of major figures, companies or organisations is perfectly normal, and won't get you into trouble.
There are no laws regarding who you can link to. You can put a link on your blog that goes to any other site, without that site's permission.
In most countries, income from advertising you display on your blog is taxable, and needs to be reported on your tax return, just like any other income. In the US, Google AdSense (if you use it) reports your earnings directly to the tax office.
Though there are no laws against these things, most blogging systems don't allow certain kinds of content. This is usually just any kind of content that would reflect badly on them.
It's worth checking with your provider before you start writing, if your topic is something highly controversial, or of an adult nature.