I am in MD (Zone 7ish) around Annapolis.  When we bought our house 12 years ago we didn't know we had a fig until a guest identified it for us; since then we have loved it.  Unfortunately, this crazy winter killed it and we have been very sad.  But today I noticed that there are a bunch of fig shoots springing up from the base of the dead tree.  I looked online and presume these are suckers, but we really want to nurture one of them into a tree.  How to do this?  Should we cut the dead trunk? Do we cut all but one of the shoots? I have no idea what variety it is.  Please advise.

I would keep 3-4 shoots for this season. You can always prune off more later on. Nothing says a fig has to be a tree shape. A bush is perfectly OK as well.

Crofton, welcome to the forum.

Go with the bush form, the survive harsh winters better. Pick out 3-5 shoots coming from around ground level and pinch off the rest. That way the energy from the healthy roots will be forced into these 3-5 shoots. They will get taller and thicker this season than if you had allowed all of the shoots to grow. And diameter growth is what you need to help increase cold hardiness.

Then, let these shoots grow until they have produced 6 leaves. Then pinch off the very tip of the shoot. This will cause branching and will push out fruit production. Repeat this as often as new shoots reach 6 leaves. By the end of the season you will have a very densely branched bush. It may become so dense that you have to thin it out in the winter, but that is OK too.

I am following the above plan on two of mine that died back to ground level. They are growing great now, with lots of branches, and are covered in little figs. When they make fruit you can post some pics of the fruit +leaves and probably someone on the forum can identify the plant for  you. But if you are like many of us, almost any fresh fig is a good fig!

Many times I've seen people in the forums say bush form is better for winter survival. I do not remember seeing an explanation as to why it is better. This idea seems counter intuitive to me.

Hi Crofton,
Welcome to the forum.
Until mid-July, a looking dead figtree can prove you wrong. So one should continue to water and fertilize the zone.
The figtree will bounce back, or be proven dead :( after that - In North Hemisphere at least.
For your tree, I would use the old trunk as a stack to tie the new shoots. They are heavy with leaves on their top and can fall and split after a rain or wind - so one should tie them to a stack .
The old trunk will as well avoid that someone walks one those weed looking treelings .
If you plan to multiply the tree, that is the occasion - keep two more shoots for airlayering purposes.
If you don't plan to multiply the tree, keep five shoots for now as a slug or whatever the damn beast (or a human foot ) could damage one of them - so you should have a backup plan just in case.
Next year, you'll then decide to keep whether three or five for a year more as long as there is space for them all - keep in mind: winter died-back might do the thinning for you - so keep up with the backup plan.
But the tree being yours, you'll have the last word on the choices you will make ( unless your Madame chimes in ... they can be terrible ) ...

 In my Zone 7, I've never got a tree to produce figs after a severe die-back - so I target the shape and an heavy canopy in that case. I went through that in 2012 .
In 2012, I had trees budding back at the trunk at fifty centimeters of height but none got able to ripen a fig - All my figtrees are in ground.

@James : Just my point of view : If you make a tree that is branching at one meter fifty of theight... For me it is impossible to protect the tree efficiently - you can look at my technique in my post about winter protections .
When I grow bushy, in the same space I protect more trees, and the branching being done at fifty centimeters, it is easier to protect more branching.
It seems to me that a figtree shaped in a tree almost looses his ability to root shoot and so to bounce back from the dirt .
I had a plan to buy a "noire de caromb" - tree shaped - I did hold back - The tree is impossible to protect in the winter for me ...
Another reason : for whatever the reason, the higher the branches, the more die-back they get - so I keep them "close" (as close as possible) to the dirt .
Ok, I know one reason : imagine the cold/cold wind slices/damages the stem at half of his height - the trunk gets a brownish stain - all the upper growth is lost ... Don't you ask me how I do know that...

Are you planning on trying to protect the trunk from winter damage somehow or just let it grow?  If you are going to try to wrap it or whatever, it might be better to have just one trunk. 

Otherwise, a bush will work fine with multiple shoots.  Main thing to think about is that you can get to the ones in the middle.  There's no point to have a huge bushy thing that you can't even access.  Other goal is to not have the leaves/branches shade each other too much.  There is no correct or incorrect number of trunks.  Each winter one or more might die.  So having more than one is insurance.  You very rarely if ever see an east coast fig tree growing as a single trunk.  The primary reason for this is that, even if it had one at some point, some harsh winter knocked it down to the ground.  Then when it sprang back it put out multiple shoots.  That's what you're observing now.  So rather than force it to grow into a single trunked tree, better to go with it and let it be a bush.