How do you know when to pick sweet potato?

I shared this picture over on my Facebook page, but I thought I'd broaden the reach and appeal to a wider audience through my blog as well!

I've shared a gardening post about planting my sweet potato vines in a place beside the house where nothing else seemed to grow well. I've even had a rogue one unearthed by the puppies, but I haven't actually done a proper harvest yet.

Sweet potato and galangal - BEFORE

They've been in the ground about a year, and the change from my tidy planting of the carefully cultivated slips, to the mess of leaves I have now is huge!

Sweet potato - AFTER

I experiment with growing a lot of things, but often I do it spur of the moment without thought of when and how to harvest. I figure I'll work that out when the time comes. I do like growing my own food as I love knowing how it was grown, and what was put on it (usually nothing as I really am quite lazy and if a plant needs lots of love, attention and products it probably has no place in my garden). I also like keeping my food miles as low as possible, and contributing to the lowering of our grocery bill. Wins all around really!

The vines are obviously doing really well. In fact, they've taken over the galangal, and they're making their way across lots of the other plants beside the house, including climbing over my raphis palm too! They're gorgeous, lush and green on top, and as is evident from the munching, also loved by my rampant grasshoppers.

My question is, how do I know when they're ready to harvest? How do I make sure the bounty is stored correctly once unearthed? Sure, I can ask google, but first I wanted to appeal to real people with real experience. Can you help? I'll update with a consolidated list of information I receive!

Edit:

• Apparently you harvest sweet potato when the top of the vine turns yellow, or before the leaves are frost damaged, as this can promote rot.
• You can also eat the leaves in things like salad and stir fries. Pick these anytime.
• Flowers can be picked and added to salads. They have a nice mild sweet taste.

How's your garden growing lately?