Tips for buying my first car?

i just graduated college and decided to buy myself a new car. when i say i'm buying my "first" car, i mean i'm going to the dealership alone since i've had my dad come with me when i bought my real first car since i didn't know how to really haggle or talk to the dealers. are there certain do's and don't that i should be aware of when talking to a salesperson? also, what is the lowest price i should go for when trying to haggle over the price. i know that i shouldn't just throw a random price out there but i just didn't know if there was some "unwritten law" out there of how to deal with car dealers. finally, im trading in my car i have now. the engine in the car was rebuilt several months ago because the timing belt snapped and the valves and a piston got messed up. should i tell this to the dealer? i want to emphasize that it has almost an entirely new engine but i don't know if it'd be kosher to mention that the timing belt snapped on me.