We just negotiated to buy our Expedition. I was offered $3500 for my trade but decided to sell it privately. We ended up selling it (2009 Odyssey) for $7200 on craiglist within a couple days. Maybe we got lucky? But I knew I could easily beat the trade-in, carvana, etc offers because my vehicle was clean and well maintained.
As for negotiating, by being patient and realistic you should get a good deal. It's nice not to involve the trade and just look at raw numbers.
I have found that dealerships will all come down to a certain price, maybe 6 to 7% off MSRP right away. They will ignore you if you send a low-ball offer of around 15% off MSRP or more, meaning they will not go back and forth. So if MSRP is $74k and you say I'll give $62k, they will just say sorry best we can do is $69k, the price that most dealers will come to easily.
They are hesitant to go lower until they know you are very serious, as they do not want you playing their numbers off of other dealers. We worked with a local dealer 10 minutes away and told him we were ready to buy today if we could get to $xxk, which was 10% to 11% off MSRP. Initially they said no, but a few weeks later we called again and came up $500 saying we were still ready to buy and wanted to stay local. They came back and said sure, but we would have to come up $750. At that point we were at 10% off MSRP and we went in and signed everything.