Before you start searching, you need to know that birth, marriage and death records are in the group of so called VITAL public records. So, when referring to marriage records you might also find them under the name of 'vital records.' Let's see if we can find those vital records online in the next step.
You can't find marriage records online for free. From exploring the records on many states, what I've found is that every state has its own offices if you want to order marriage records. But you'll have to do that offline not online (and I suppose you guess...that's not free at all). How to find where you can order a record? Simple, use Google. Just write "[name of the state] marriage records" or "[name of the state vital records." For example, "Minnesota Marriage Records." But that's not enough. To filter the results, read the tip in the next step.
Usually when you search you'll get lots of results which will lead you to some paid...untrustworthy sites. To see the official site for that state, look at the URL. Usually you'll see it ending on .us or .gov. So that's how you do it offline. There is a way to do this marriage records search online too. You can see the divorce dates and information like that. It just costs money but it's quite cheap. Read that in the next step.
There are lots of scam companies out there giving false promises to deliver up-to-date public records. Fortunately, there are also some good companies working for years. They have their own representatives going to the state offices for you and requesting the records you need. One of them is US Search (link below if you scroll down and you'll see a text called "Resources") where you can conduct a complete background check on a person and get all the possible records on him.