First, educate yourself regarding the cemetery you will be visiting:
Are rubbings allowed?
Are certain rubbing materials forbidden?
Get permission to do rubbings

Preparations

Supplies

water bucket
Large sidewalk chalk, many colors
pelon fabric
masking tape only (no scotch or duct tape!!)
paper and pencil
gum eraser
wooden popsicle sticks
camera
large pieces of cardboard, covered with aluminum foil.
large paintbrush, stiff toothbrush (NO WIRE BRUSH OR SCRUB BRUSH PLEASE)
non-ionic cleaners (no household soap or bleach)

How to Preserve Tombstone Information
Rubbings
Assess the condition of the stone to be copied. Older stones are often made of soft limestone, easily crumbled or distorted with mild pressure. Look for cracks, flaking or any sign that pressure might damage the stone. If any flaking or possible damage will result, do NOT continue with the rubbing. Preserve the tombstone record with a photo only.

Cleaning the stone

If tombstone is in good condition for a rubbing, clean the stone. Brush with dry paintbrush to remove any debris.
Use toothbrush to gently remove any debris in the carving. Pre-soak tombstone with water, to loosen stubborn dirt. A gentle soaking is sometimes all that is needed to clean stone. After presoaking, lichen can often be removed with a gum eraser or wooden popsicle sticks. If additional cleaners are needed, pre-soaking will prevent the cleaners from soaking into the stone.
If additional cleaning is needed, use only non-ionic cleaners on the stone. Gently rub cleaner on the stone, starting at the base. Rinse frequently.
Do not use excessive force when rubbing on the stone.

Rubbings
wrap pelon fabric across the part of the tombstone you wish to copy.
secure the pelon in place with masking tape, so fabric is held tight to the stone.
Gently rub in one direction, with colored chalk across the pelon on the tombstone. This will show the tombstone as the chalk color and any carvings will show white. [See image]
Using pelon has two advantages - you don't leave any chalk on the stone, and you have an image of the stone on pelon to take home.

Copying the Data from the Tombstone

Write down the name of the cemetery, and the date of the visit.
In large cemeteries, indicate what section stone is in, and how to locate the stone.
Write a brief description of the stone, it's shape, images and color.
Copy exactly, the inscription on the face of the stone. Do not correct any spelling errors, just copy as found on the stone. [put your comments on the side, in brackets].
Indicate the direction that the face of the stone is facing (north, south, east, west) Walk around the stone, and copy any data or images found on the sides and back of the stone.
Copy any saying (Rest in Peace etc) that is found on the stone.
Look on the base or foundation of the stone, for any carvers initials.
Look for any footstones on that plot.
Make note of the names on adjacent stones. (Not only will it help you to locate the stone in later years, but the adjacent stones could also be unknown relatives)

How to Photograph Tombstones.
Outdoor photos will be more colorful, if taken on a cloudy day. (less glare)
Try to have the sun at your back, but at a slight angle, (5 or 7 o'clock) so that there is a shadow in the lettering on the stone.
Prop up aluminum-covered cardboard to reflect light toward tombstone.


A word to the wise

Leaving the cemetery in the same condition that you found it, goes a long way towards paving a path for the historians of the future. It only takes one rotton person, to leave a bad impression on a cemetery and its groundskeepers. Pick up any litter or trash. Do not leave any sign of your visit. Do not give any caretaker the grounds to bar future rubbings or unsupervised cemetery visits. We all know of courthouses, that have barred genealogists after damage was found to public records, so be wise and treat the stones with care. They may be stone, hard as can be, but they still can be damaged.