Hi. I bought three tubers of Dahlia Verrone's Obsidian from a reputable garden centre so they are of good quality. However, they were reduced as the planting time is given as March to June ("sell by" date), and they have sprouted. The shoots are a couple to a few inches long are upright and look healthy, although they might be thinner than they would be if planted. Bearing this in mind, how sould I plant them - with the bottom of the shoots slightly below, above or level with the soil?

It is funny that this should come up. I too, just bought Dahlia bulbs. If you look at them closely, the new green shoots come from the top 25% of the tuber or bulb. That is the end you should plant near the surface. The other end of the tuber should possess the vast majority of the roots.
From what I read recently, I am using containers but they could be planted in beds on the ground. I am using Miracle Grow potting soil. The planting time should be after the soil temperature has reached 60 degrees.
They like, prefer, morning sun, well watered but never soggy or wet. Do NOT fertilize right away. Wait a couple of weeks. They should bloom by mid summer right up to first frost!

Does that mean some of the stem should be covered by the soil - I don't want it to rot.

Yes, but not by inches. Don't plant them 6 inches deep, just barely enough to cover the tops of the tubers.

As I have said previously, don't go heavy on the water ever. They should get watered just a bit while starting out and when the new shoots are 3" or so, you wont be inclined to rot them.
Keep track of when Mother Nature helps with the watering. Only water when they are starting to dry out. Keep it in mind that the tubers purpose is to store moisture, keeping it in reserve until the new shoots start. They might actually shrivel a bit but as they actively grow for the new season those tubers will plump up and they will make more tubers for the next year.