The dataset you mention is a shapefile, a format invented by ESRI, but understood by most GIS software, including Quantum GIS.
After extracting the zip, you can add it with Add vector layer and point to the .shp file. The CRS information is stored in the .prj file.
With the openlayers plugin, you can add a Openstreetmap or Google background layer. For doing that, you have to set the project CRS to EPSG:3857.
If you want coordinates in lat/lon degrees, just rightclick on the shapefile layer, and Save as ... to a new file under a different name, selecting EPSG:4326 as CRS for that, and check to add that layer to the canvas. Saving may take some time.
For the next step, you better zoom in to see just a couple of points. Open the field calculator, and click on the pencil symbol at the bottom to enter the edit mode, and then the field calculator icon bottom right. Create a new field named degx, type real, precision 6, and select $x from geometry. After saving (which takes some time), do the same for degy and $y.
The new columns give you lat and lon in degrees.