How did they edit photos of celebrities and models before computers were invented?

It's called post processing - 'editing' is the process of deciding which images are used. Yes it's amazing isn't it, how photographers managed before Photoshop ;^p There are many darkroom techniques that have been brought over into modern software - air brushing, dodging, burning, masking & layering are just some of those we used to do in the darkroom. It's just a lot easier now with software. Of course the correct thing to do is to get your lighting & exposure right in camera - to minimise any post processing.

The photographers shot using transparency film and they had to be on the money when they exposed and composed their shots. Very little was done in the area of retouching because like now, it was very expensive to hire a retoucher. They used air brushes and other techniques to modify a photographic print is any thing had to be done to the image. Editing was that act of placing all the transparencies on a light table and sorting the best from the rest. Models, like today spend a couple of hours in make up and hair styling getting their face and hair just perfect before the photographer starts taking their shots. There should be NO need for post except to cover any mistakes the photographer may make. Photographers that hand in poor work are just not hired again.

I'll give you a hint: There is a reason there is a tool in Photoshop called the "airbrush" tool.

Then, as now, there were specialist retouch artists. They worked directly on the prints with inks and dyes or in the case of large format film would sometimes work directly on the negatives. Also specialist printers would do a lot of work in the darkroom on the prints.