There is a special rubbing paper available to monument shops that has its ink contained within it. All you have to do is put the paper to the stone and rub it with your hand and voila! You might find it a trifle on the expensive side for everyday use, though. It is better than rubbing the stone with a crayon or charcoal, if you can afford it.

Speaking of rubbings, I have a rubbing of Shakespeare's epitath, certified by the sexton and done in 1938. It appears to be black crayon on brown paper.

Oblique lighting can bring up letters nearly obliterated by time and weather. You have to work at getting the right angle, though. And then take a picture!

Don't use ANY liquid on a stone if the temperature is or will soon be below freezing! Water, etc. can freeze in letters and surface cracks and destroy the stone and/or its carvings! Don't do it! (Warm weather is different.) Repairs can be minor to costly to impossible.
Been there, seen too much such damage. Remember, it might be rock but it ain't indestructible.

Something to look for when you're looking a stones: a V shape with smooth sides will nearly always (on a granite stone) indicate that a chisel was used to make the carving. A V shape with bumpy sides and a small "bead" at the bottom (like a V with a little rounded thingy instead of a sharp point) indicates that it was sandblasted. Sandblasting, of course is far less expensive than carving and more recently used (around 1920 in most places). That's on granite, marble is a different matter.