tl;dr
There is no normal in this scenario; one will dig as deep as the hole can get meanwhile others will just stick with peeking on your CV and contacting the people that recommend you. Although, most employers will Google you before your interview.
So
It's common todayReflecting on what many say, most employers (>80% according to that huffington post article) do indeed Google you are search-engined before you're hired/interviewedinterviewed, andprobably with the intention to see if there's anything negative about you that stands out.
If your social media accounts are public then you should assume that you're looked up and your views are taken into account in the recruitment process.
Why wouldn't they? It's free information that could spare them a great amount of money. One might argue that this is not ethical but since there are no laws about this then there's not much you can do about it -- expect hide what you wish to remain hidden.
This question is really about how separate should we expect private life and professional life to be in 2015.
You have no private live when your name is associated with it, especially on the internet. Always imagine that everything you say on the internet, or in general really, will appear to your employer's desk in a regular report. Don't say anything you wouldn't want your employer to see, or ask yourself whether you'd like your parent to see what you're about to submit or not.
You can't really ask what does every HR person use to find information about me? since it's individual based but the rule of thumb that you should stick to is: