Buying a house

I'm looking for a house, and would like some advice from someone with experience in the process. The morgage/funding side of the equation is taken care of, but otherwise, I have absolutely no idea what I'm doing.

I'm going to be buying someplace inside the loop, most likely in the montrose area. Price range is $275,000 - $325,000, which means I'm going to be getting something old, unless I get some kind of townhome, which I don't want as I want a yard. I've been looking through the HAR listings so I know what's available.

How does the process of contacting, showing, inspecting, and closing work? I'm assuming fair value would be something like HCAD.org values, plus a bit, assuming there's no problems. Is this unrealistic? Any general advice would be appreciated, as well.