Firstly, I think the blacked foliage initiates rot. I've no proof either way, its just a gut feeling, and I waited for frost once only to find the first freeze came with a foot of snow! I was forced to leave them in for too long and lost some stock. Secondly, I have little spare time and need to get some of my Narcissus in. But the Dahlias are in the way!
Techniques vary I imagine, but this is how I do it.
I chop the top growth to eight to ten inches above ground. Chopping to above a node is not required at this stage as the tuber will be trimmed again before storage. Then lift the tuber with a spade (I find forks damage the tuber sometimes). Once the tuber is free from the ground, use the remaining stem to lift it up (don't be scared, they are usually tough). I then grip the stem with one hand and whack the top with a rubber mallet or block of wood to loosen the soil from around the tuber. Make sure you wire on a label at this point too. Line a tray with newspaper and just lay it in angled with the stem down, not to densely though as airflow around the tuber is vital. I then put the tray indoors to 'dry' the tubers for a week or so (I use the utility room)
For storage I just leave in a very open basket or tray, indoors over winter (utility room cupboard actually).