I go in looking very innocent and start off by being vaguely interested, but not sure. Let them convince me I need a new car.
So last car we got around 1k off. We started with them asking 7K, I offered 4k, and we discussed it from there. I knew I'd have to move a lot. Start lower than you want.
But they also paid the year road tax, new tyres all round, replacement number plate (one was cracked) a couple of places which were scuffed they sorted, replacement windscreen wipers, replacement brake pads on the front (backs were like new, I checked) and a replacement handle on one of the seats, which was missing.
I regret not asking for replacement spark plugs (as we ended up replacing them within the year) and would ask for that too next time.
I did also ask for a full tank of petrol, but they stuck at that point.
What I did was was interested, but not over enthusiastic. They knew we were talking to other garages which isn't a bad thing to drop in.
Started by test driving. Asked lots of questions about what things were for etc. Give them the idea you don't know too much. Then look over the car. I'd ask things like "have the tyres been fully checked, this one looks a bit low on tread" and they'd respond with "we can replace all the tyres for you." Commented that the back brake pads were good, had they changed them and they offered to change the front ones as I went to look (I think they knew they were low)
Then we went in to talk and I was all "why was that apparently identical car over there cheaper? Can you bring this one down to that?" (other car was 4k) They then said not that far, what was I thinking around.
I stuck on about 5.5k for ages and said we'd have to think about it as that was more than we wanted to pay, and they then suggested if we paid more they could do things like the tax bill. They also upped the amount they'd pay for our car (which was only ready for scrap so not worth anything), so although we ended up paying 6k we got other things off.
It did take quite a long time. You need to be prepared to chat about nothing, have a drink, discuss other things.
Dh was a mix between totally embarrassed and in admiration. He hates negotiating.