Pre-soak the dry Shiitake mushrooms in a bowl of very hot water (e.g., just boiled), with stems facing down. The bowl should be at least half full of water. Expect the mushrooms to float in the water. Let the mushrooms soak for at least an hour or until completely soft.
Chop a little bit off the end of each mushroom stem, then slice the mushrooms up (cap and stem) into long thin strips (or diced sized pieces depending on your recipe).
The amount of time it takes to rehydrate dry Shiitake mushrooms really depends on their size. If the Shiitake mushrooms are small, they could be softened enough for cutting within 20 minutes if placed into hot 'just boiled' water, giving you just enough time to rehydrate them on the side while prepping other ingredients for cooking. So check the size of the dry Shiitake mushrooms you have on hand when planning the amount of time you need to rehydrate them.
If you have plenty of time, use cold water to soak the dry Shiitake mushrooms (but expect it to take longer to get the mushrooms completely soft and ready to use) as this minimizes flavor loss from the mushrooms into the soaking water. I often just put them in a bowl of cold water, and place the bowl in the fridge in the morning, so that by evening time, the mushrooms are already soft and ready to be used for cooking a dish for dinner.