Bring a family history book or old family letters or journal along with you and spend some time telling stories about the deceased person. You might choose to visit the grave every Memorial Day if you live near by. Memorial Day is celebrated in the USA on May 30th but you could observe this day of remembrance regardless of which country you live in. You could also use this time as a family service project to clean off the grave site. You could bring flowers or send the flowers to their surviving spouse or child as a tribute and remembrance.
Many tombstones have interesting quotes or sayings.
Hold a piece of paper over the stone and rub the side of a pencil lead back and forth across the paper with gentle pressure. If you want to preserve your etching in a scrapbook or frame, use acid free high quality paper and chalks. Archival stores also offer a spray that will protect the paper etching and help preserve it. Children love this project but will get discouraged if you do not have everything needed to start and finish the project quickly. Be prepared with all of your materials needed ahead of time.