I usually use a combination of the classic websites (BeenVerified or InstantCheckmate), and Google searching their name(s) with keywords such as: 'lawsuit' 'arrest' '_____ county jail roster', etc. If you are more suspicious of a person or the transaction is quite sizable, a private investigator may be your best solution.

One of my companies, Thurion Diligence, specifically does this. I use it for all my acquisitions and talent. As someone who has intelligence experience, done a search, acquired, and operated a company, among other things, I know exactly what corporate diligence should look like. You can get cheap surface-level background checks, but most will not know what to look for or what needs further evaluation. Depending on the business and the position, others may require continuous monitoring.