I actually spent a rather stressful evening before my doctor appt reading previous clinical studies involving aspirin, trying to figure out what to do! Basically aspirin has been shown to help (they think) but it hasn't been tested on a large scale, which is what this trial is intended to do (it's worldwide, I believe). The amount hasn't really been agreed either. At the moment they're recommending 75mg a day, but they don't even know if that amount is enough.
In my situation I had the 12 week scan and my first blood test, and they said they called me the next day to say baby was negative for down's but I was positive for pre-eclampsia (which wasn't surprising as my mum had it and I have hypertension anyway). At that point I was asked to come in to discuss before agreeing - it sounds like similar has happened for you? It was at this appointment, once I agreed, that they gave me the pills. I was given a sheet to record any "unusual" symptoms (ha, I'm pregnant, everything's weird, but thanks).
I was called at 16 weeks to see how I was doing, said I was fine. At 17-18 weeks I felt awful so rang them up (after trying in vain to get help from my midwife) and they got me in for a scan that day, went through everything with me, did my blood pressure, etc. I had my 21 week scan and everything was normal (although there's a problem with the cord that could develop in the future). As everything looks fine, I'm not due back until 28 weeks. But I can call them any time with any issues and they'll check me out, which is reassuring.
Whereabouts in the country are you?