The 'det är' construction

Swedish as a language is very interested in whether things are known to the listener or not. English is too, as compared to languages that don't have the category of definiteness. But sometimes I feel that Swedish takes this obsession just a little bit further than English does. We just take very great care not to shock the people we're talking to by throwing new concepts at them.

In Swedish, when we want to introduce a new concept, we use the construction det är. det in this construction does not refer to the thing introduced. How could it, since that is a new topic that is being introduced to the listener? It would be very illogical to start out by mentioning the gender or number of a thing that has not even been mentioned to the speaker (or so native speakers of Swedish feel).

Therefore we say:

Det är ett hus 'It is a house'
Det är en bil 'It is a car'
Det är mamma 'It is mom'
Det är mina skor 'They are my shoes'

The det at the start of those sentences does not refer to the house, car or whatever. It is a formal subject that is used to introduce a new concept. It is like the it in 'It is raining'. You could also say that the det here stands for 'what I am going to tell you about next'.

About the use with people – you do something similar in English, as my good friend ViArSkoldpaddor once pointed out: if there's a knock at the door and you know who's there before seeing them, you would say It is my wife, not She is my wife. So with people, the idea is that if you are already talking about a person, and just want to add some more information about her, by all means say Hon är ….
Example: Hon är inte bara tandläkare, hon är min mamma också 'She's not just a dentist, she's also my mom' (to paraphrase a commercial from some years back). But if you're introducing someone for the first time, you say Det här är min syster or in English 'This is my sister'.

About the use with plural: in English, you obviously want the pronoun to agree with the thing introduced. Since you don't have a plural of it, you have to make do with they. In some cases those also works.

So, is it ever possible to say things like den är en bil? It is, if den refers to something that has been mentioned previously in the same sentence. Min bil är inte snabb, men den är en bil. 'My car isn't fast, but it is a car' could be one example.

There is also the case when you point right at one of several items, and stress den when you say den är …. This context would be better translated into English as that one is …. Like, imagine you have several tools spread out on the table, you point at them and say That one is a hammer, that one is a screwdriver … 

In the cases where the pronoun refers back to a preceding clause or idea, you must also use det. I'll borrow an example of this from Latif_ in this thread: Vi behöver betala högre skatt, eftersom det är en bra idé 'We need to pay higher taxes, because that is a good idea'. Here, det does not refer to the idea, and not even to the tax, but it refers back to the entire previous clause, so it must be det.

As you may know, this in Swedish is det här or detta, and that is det där (or sometimes just det) . We use those expressions according to the same principles as det in presenting constructions. So you say Det här är en bil for 'This is a car', not den här. And Det där är ett hus would be 'That is a house'.