Grandpa, tell me about the time that Uncle Edgar tried to teach you to drive the Model-T Ford. That kind of question gives your informant a definite direction. Try not to interrupted a story with questions. Save those for later. By the same token, make certain that you have enough tape left in your recorder to get the entire story without having to stop to flip the cassette.
Nothing is more unnerving to the storyteller than to have to pause in the middle of a narrative.
Once your tapes are recorded, make a backup copy of each one as a safeguard. Some people like to make a transcript of each tape, but that is a slow and painstaking process. The advantage, of course, is the convenience of having a hard copy of the story available. Store your tapes in their plastic boxes in a cool, dark place where the humidity stays relatively constant. Better still, consider depositing the original tape in an archive.