In our hospital in Northants women are counselled when they have their booking appointment with their midwife and can choose whether they would like to have Downs screening or not. If they do then they are booked at 12 weeks for a nuchal (and dating) scan, if they dont then they just have a dating scan.
Has your midwife asked you about this? You could try ringing your ultrasound department tomorrow and asking what type of scan you have actually been booked in for and if they do nuchal scans? If they dont you can get them privately but they have to be done before the baby is 84mm long (14 weeks 1 day), so you would need to get that sorted asap!
The procedure at a nuchal scan is fairly similar to a dating scan as described by melliebobs. However, in addition, the sonographer has to get a good measurement of a fluid area under the baby's skin at the back of the neck, and this can take some time to get, as baby has to be in a good position. This can involve turning you from side to side on the couch, tipping you head down for a short while, sending you to the loo to empty the full bladder we asked you to have!, or even sending you off for a short (10 min) walk.
If the measurement is successfully obtained and your baby is within the length range (45mm - 84mm) then you will have a blood test as well. You will get the results later - in our hospital it is within 2 weeks.
Hope this helps - I am a sonographer who does these all the time.