I've bought a few cars now as a single female and work in an industry related to car sales, so I know a bit about what is happening behind the scenes.
This last time, I emailed the dealerships with very detailed specifics of the car I was looking for, told them I wasn't interested in a lot of back and forth and wanted to know their best offer. I immediately blew off anyone who emailed me back saying "come on in and we'll discuss color and what kind of deal I can get you"

(Yes, there were some of those) I also blew off the dealerships that said "let us know what the best offer you get from other dealerships is, and we'll beat it". Umm - no, that's not what I asked for, and I don't want to deal with anyone who can't listen. But I did end up with a couple of dealerships that took me seriously and sent me offers. And one of those clearly went straight to their best offer. It was actually a really good one (I had researched invoice values and incentives ahead of time through the various websites like Kelly Blue book, so I knew what a good price was when I saw it.) I went down there, found their internet sales person, said show me the car and that was that. We negotiated a bit over trade in, but I was in and out in less than an hour.
Note: I had financing ready to go through my credit union, which I let them know, but I also gave them the opportunity to top it. I ended up getting a 0% loan through the dealership, on top of my amazing deal.
The key things to remember are (1) research, research, research the cost of your car ahead of time. Be aware that the "invoice" cost is not what the car costs the dealership - there are all sorts of dealer incentives and hold backs from the manufacturers that they will get on a sale. If you aren't looking at a high demand car, you should be able to get invoice cost OR BETTER in some cases and (2) walk away from anyone who won't take you seriously. If you ask to see a bare bones model and they claim not to have any and try to show you the loaded model, tell them thanks but no thanks and walk away - don't even let them get you to look at the loaded ones. Leave a phone number if you want, they might surprise you by suddenly "finding" a bare bones model for you to come look at.
There are also car brokers you can go through, if you have no luck with the dealerships. I bought one car that way, and had a good experience. They go pretty quickly to their best offer, and don't seem to play as many games. You might want to try something like carsdirect.com, just to see what sort of results you get.
Finally, if you can wait a bit, try to hit the dealerships towards the end of a month when the salespeople are sweating hitting their numbers so they are more willing to make a deal. Better yet, wait until the end of a quarter. Unfortunately, the first quarter ended on Thursday, and we are heading into peak buying season, so this weekend was probably one of the worst weekends to be looking - they just aren't as desperate.