There are a 3 main ways you can background check these days. Some are expensive, some free, and others in the middle.
Here are the 3 methods:
Visiting all of the government offices and gather the records. You can get quick results; some people may be surprised to find that a simple request to the right person will yield a lot of public records on someone. Most of the time you can get these records immediately but depending on the backlog you may have to wait a week or two for them. Usually there is a small fee involved for paper work.
Hire a Private Investigator
Another method is hiring a private investigator. There are so many private investigator agencies in your area, but hiring an investigator is expensive. If you have the money this may be an option for you but be sure to hire a professional detective.
Out of all three probably the best solution for most people is to sit down at their computer and access public records online. This can be a reasonably cheap and sometimes it is absolutely free. It doesn't require driving all over the place or lots of money. There are a number of websites on the internet dedicated to this kind of searching. Most will require a small fee but will generally provide all of the records in one place.