I'm not familiar with the OM-10 so I looked it up. The OM-10 is an aperture priority camera only. This means that you pick a lens aperture (opening) and the camera picks the shutter speed. With a normal lens (50mm) you can handhold the camera down to 1/60th of a second. You may be able to pull off 1/30th if you are real steady or leaning against a tree or something. So pick an aperture and check the meter to make sure you are shooting at 1/60th of a second or faster and you are good to go.
The faster the shutter speed the better you can stop action. The slower the shutter speed the more you blur the subject. Ever seen a photograph of water flowing where it looks like fog? It's because the photographer used a slow shutter speed.
The smaller the aperture the more depth of field you have. The larger the aperture the less depth of field you have. Ever seen a photograph where the background is blurred behind a pretty girl. The photographer used a large aperture.
On a fully manual camera like my daughter's OM-1 you control both shutter speed and lens aperture. When you change one you have to change the other to compensate. Otherwise you will get a photograph that is either under or over exposed depending upon what you did. On your wife's OM-10 all you have to do is pick the aperture and the camera picks the correct shutter speed.
I started out with a camera just like yours except mine said Canon on it instead of Olympus. After I learned what I was doing I sold the camera and bought one that had full manual controls. Since you have lenses for the OM-10 just learn on that and later buy an Olympus that has full manual control later. That way you can use the same lenses.
I know what I wrote sounds complicated but me and the rest of the us on the forum were in your position at one time. We all learned. It's not hard at all really. I mean, we learned!
What I would do is go on eBay and buy yourself a cheap used instructional photography book for 35mm photography. The book will have plenty of pictures in it to help show you what it is telling you.
Most of all, have fun! Welcome to the forum.