I've bought five cars from dealers, all new or less than two years old (all for other people - my mk 5 GTI is nine years old). Here's what worked for me, every time:
1 Decide on the exact model, spec, mileage.
2 Find three matching cars, at different dealers.
3 At 9am, turn up at the dealer furthest away and ask for their best price. If you have a trade-in, make sure it's there, shiny and with service history.
4 Armed with the first dealer's 'price to change', repeat the exercise at the second dealer. Tell the salesman what the first dealer offered and point out any differences between the first car and the second (whether it's to your advantage or theirs - it removes any bargaining power they may have). When you get the second price to change, tell the salesman the price quoted by the first dealer and ask them to try again if their price wasn't already better.
5 Repeat step four at the third dealer and tell them that they are your preferred choice because they're the closest. However (you say), the first two dealers will deliver it for free, so they have to beat dealer 2's price, not just match it.
I never tell them what I do for a living even though I'm not in the trade. I just smile or say I no longer work (how I wish that was true!) I never appear too keen or in a rush. It's simply a business transaction - there's no emotion involved.
One day of this has never saved me less than £1,000 and often more. Try to enjoy it!