What is the best way to view a hard to read headstone?

Shaving cream
When using shaving foam, be sure to use one for "Sensitive Skin" as is less acidic than the regular foam. Remove the foam with a rubber squeegee (no metal parts) and the foam will be left in the indentations. Take several pictures from various angles. Be sure to rinse off the stone with water from a container you carry with you. Some people are concerned with the acidic nature of the foam, but it is considerably less acidic than our current rain and certainly less than the bird poop deposited on the stone over the decades.

Foil
Another method commonly employed, is securing light aluminum foil in place over the stone and then pressing on or rubbing the foil with the heel of your gloved hand. The foil should take on the dents in the stone. Tape the foil to cardboard and file it for later reference in the quiet of your study.

Etchings
Making an etching with newsprint and chalk or special grease crayons.

Water
Simply wetting the stone with water and using a soft brush to clear way the detritus will also work wonders.

Mirror
Use a small hand mirror to direct the sunlight at a steep angle across the face of the stone. This highlights the carving and makes it easier to read.

Dear Ancestor
Your tombstone stands among the rest;
Neglected and alone.
The name and date are chiseled out
On polished, marbled stone.
It reaches out to all who care
It is too late to mourn.
You did not know that I exist
You died and I was born.
Yet each of us are cells of you
In flesh, in blood, in bone.
Our blood contracts and beats a pulse
Entirely not our own.
Dear Ancestor, the place you filled
One hundred years ago
Spreads out among the ones you left
Who would have loved you so.
I wonder if you lived and loved,
I wonder if you knew
That someday I would find this spot,
And come to visit you.

Author Unknown