Sunny days are NOT what your camera wants. You and I may enjoy the sunshine, but the camera cannot cope with the high contrast or difference between the brightest sunny spots and the darkest shadows. A bright overcast day is better, and a darker, cloudy day is not a Big Deal to the camera.
Using a flash adds light, and if the face of the headstone is in shadow, it can help to reduce the contrast. However, I have had mixed results and find that proper exposure on the face may cause the background to over- or under-expose. Sometimes the flash creates some unpleasant glare reflections from shiny bits in the stone and the natural lighting looks better. That said, I often take two photographs, one with flash and one without, and decide which looks better later.
Sometimes you get lucky, and the markers are in the shade. Usually, the headstone you have hunted is only partially shaded, or not at all. So, bring your own shade. You may be able to shadow a smaller marker with your body, or somebody else, but be sure that you shade the whole stone. I have used a folding, lightweight car windshield shade, which us usually the right size and easy to carry along. A large golf umbrella might also work for you.
Me and my shadow
Sometimes, if you just cannot avoid seeing your shadow, a bit of editing the photograph can “repair” the photograph, particularly if you deliberately leave a little more room for editing.
Of course, sometimes there is just no no way to “repair” a photograph!
Look for angles that eliminate, or at least minimize, any objectionable shadows.
A smile is not a frown turned upside-down
I had a great idea to keep my shadow out of the picture, I could just turn the camera upside-down and I would not be in my own way. Well, as clever as this sounds, I do not recommend that you try it. The next photographs show the results of my cleverness. Something Just Does Not Look Right in either photograph, the writing is upside-down in the left and the dandelion is growing upside-down in the right!
Oh, and these photographs demonstrate why I now leave a larger border around the headstone.
There are many ways to ‘tell’ your camera which part of the photograph is important, so that it selects the proper exposure for your subject. These include Spot metering, Center weighted metering and Matrix metering. A white card, or grey card, can also help. There are too many variations to cover here, but do consult your camera’s manual for information.