@Rebecca PetersThe deal came to me from a realtor friend of mine. It was on the MLS. Actually, the way I found it was that I came across another property that was right next door to a property that I currently own. It was also on the MLS. I saw that the listing "broker" was the father of this friend of mine. I called him up and he told me that the property was already under contract, but that they had another one available for me to look at. And that is how I found it. It shows the power of having a strong network. Had I not called my friend about the other listing, I may have never found this property.
Regarding communicating with the tenants, I just sent them written notice prior to closing that the property was being sold to new owners and new instructions on how to pay rent, then after collecting the first months rent (as a reserve), I sent a follow up letter letting them know that their rent was being raised, and just waited for calls to come in.
If your tenant is paying below market, chances are they most likely know it. They will obviously not say anything to you about it. Should you serve them a notice of increase in rent, it will not come as a surprise to them. They will then either make the call of staying or finding another place to live that they can actually afford. As long as you are civilized and work with them on it (i.e. give them ample time to find a new place, weigh their options, etc.), you shouldn't have any problems.