if you are completely replacing the Dish satellite system and no other TV's depend on the satellite dish feed as a source, then you can reuse the coax...it's high grade RG-6 or its equivelent. It is not a continuous run from the TV's back to the roof top....somewhere in the system was the original set top box, splitters, or a distribution block and the coax will need to be connected with "F" connector barrel connectors to re-establish a continuous run. Since you mention you are not a "cable expert" this may not be a very good beginners do-it-yourself project.
If some of the TV's in the house are still hooked to satellite, then it is a much more complicated case to determine where the coax is connected to a splitter or distribution block....but in any case, it probably would not run all the way to the satellite dish. If this is the case, you will need to run a new RG6 coax line to the new OTA antenna, then split the signal between the two TV's.
Go to www.antennaweb.org
and put your full address in. This will give you an idea of what stations are available in your area, where they are in relation to your house, and how large an antenna you will need to get the signal. A typical coaxial splitter reduces the signal to each TV by about half....so the antenna must have enough gain to get a strong signal each TV.
a good reference to installing outdoor antennas from Channel Master