I honestly felt exactly the same as you. I hadn't bought a single thing, I was so worried there would be something wrong....before I went in my heart was racing and I felt really tearful, it was just so overwhelming. I think 20 week scans are scary enough with one baby, but with 2 you are willing them both to be perfect.
re the technicalities, it can take up to an hour I think, the scanning dept will have booked you a double slot so don't worry if it seems to be taking ages, they need to be thorough and check everything on both baby. our sonographer was really good and talked us through everything she was looking for etc so we were lucky that there weren't long periods of silence which would have worried me. there's nothing stopping you from asking when you get in there if they could explain everything to you as it will help keep you calm
I found out what I was having, but if you don't want to just let them know as soon as you get in there. don't forget it is an anomaly scan, not a sexing scan, so if they can't tell because of the way they are lying I don't think they would go to any lengths to find out. although, with twins, depending on which type they are, you will have another scan in 2 or 4 weeks anyway, by which time they might have moved.
when I had my 20 week scan my boy was sat on my girls head, and so the sonographer couldn't check her brain properly, so I was told to go for a walk for 20 mins and eat something sugary (chocolate bar and fizzy drink) and when I came back they had both moved so she could carry on. don't worry if that doesn't work, they can always rebook you for another scan a few days later to finish the checks they need to do.
I know it is so much easier said than done but try not to worry, after my 20 week scan I relaxed so much and finally let myself start believing I was going to be having 2 babies! you will be fine 