hello Karen,
dark, cool but frost free , and not damp and mouldy . If you give them light they will sprout !!! If you store them in bags ,make sure they are either paper or sacking , and check for rot every now and then . Trays are better as you can see instantly if any go manky. Also make sure where you keep them is vermin free ....rats make a hell of a mess of them . All varieties that I have grown have stored ok . Just make sure you only store disease free tubers. About hens egg size or a bit bigger is ideal , but no need to worry too much about size with main crop types.
Thats how I do it , and it has always worked so far . Hope it helps ...
cheers
Russ