Cooking snails properly is somewhat complicated and can be a long process. There are many different ways to do it. If your Grandmother says this way is wrong may Grandmother would like a word with her.
Picking snails out of your garden won't get you a lot of them. They like to hibernate all Summer, so the easiest way is to wait till the first heavy rain in September or earlier depending on your climate. You'll find them hiding under rocks on stone walls. Just turn the rocks over and pick them off. A sack or two full of them in a day is not uncommon.
Now they need to 'fast', because some of the grasses they eat are poisonous to us. Hang them up in a sack like the sort they use for onions. Leave them there for 2 weeks. I have never fed them anything. Feed them cornmeal if you wish but don't blame me if they taste gritty.
Before you actually cook them they need to be cleaned. Let them soak in a pot of water overnight. The water will turn a slimy grey. Replace the water and bring it to a boil. Put the cover on because some will try to escape.
Now have another fresh pot of boiling water ready. When the current water turns bad put the snails in the other pot with the clean water. Continue cooking them until they come out of the shell.
Now you can either pull them out of the shell and fry with lots of garlic and oil or make a nice stew with red wine, tomatoes, olives, capers, mint and tomatoes. Pull them out with a toothpick like Ramm9 said above. The snail's body is in two parts. The lower part is a sort of intestine that some people find disgusting. You can pinch this part off inside the shell if you don't like it, but it is safe to eat.