If you're gonna buy new and have the credit, there's no reason not to shop the manufacturers financing available at the dealer against your credit union. There are still some occasionally hot promotional financing deals available through the manufacturers.
The best way to buy a car is to do everything off the lot (except the test drives). Research online, know what you want in advance and what it should cost, email dealerships and online buying services for price quotes and to check availability, and if you must negoitiate, then negotiate over the phone, never in person and never ever inside the dealers' sales office (where they will have you trapped). Whatever you do, just don't play the dealership game.
As for test drives, schedule those in advance, take the test drive and then quickly and politely leave (do not go back into the building/sales office).
The ideal arrangement is that when you go to the dealership to buy the car, you're just coming to sign for it and pick it up. Everything else -- price, financing, trade-in, etc. -- was all negotiated and agreed upon in advance. If the dealer tries to pull a fast one and change terms at the last minute, you get up and leave, and buy elsewhere.
At all times, you want to be the one in control of the transaction. But remember to be reasonable and unemotional, and FFS don't deny the salesman from getting at least a little bone, he has to eat just like you do, and graciously giving him at least a small piece will make him work harder for you.