Program for turning old movies to Remastered HD?

I was in the store today looking at an amazing 1080P TV and saw a very old film on it that looked..... ORGASMIC! 
I was wondering what program these companies use to remaster these films with such jaw dropping details. 

Also around how long it takes to render them? 

Well, a quality job would be done by digitally touching up and enhancing every frame. There really isn't a way to automate the process without a very intensive and complicated series of algorithms. It would take a long time to do it by yourself.

Most films and even current films are recorded on 35mm film. Which is an analog format, the equivalent digital resolution can vary but I have read that it can go up to 8-20 Megapixels. As far as I know, 4K UHD resolution can generally display all of the details that could be on a 35mm film. So when they make these "old movies" look better all they are really doing is just creating a higher resolution digital version from the 35mm original. Every time digital formats increase in resolution, they derive a new digital version (480x360, 720x480, 1280x720, 1920x1080, etc.)

In addition to that, they also do what brennanriddell said, they enhance each frame by removing visual noise and other anomalies. It's not easy to do properly and having it look good would be extremely difficult.

Ah, Thanks for the info guys! Learn sommething new every day :) 
Always thought there was some expensive program used to do it.

 

in the book pirate cinema by corry doctrow, this is explained in detail.