Start with the basics. Check the air pressures in the tires. Does everything at least look straight and even? Is the steering wheel dead straight when the wheels are straight? Check the date codes on your "new" tires. How new are they really? Now check for any play (looseness) in the front and rear suspension. Is the car level or is one side higher or lower than the other. You can tell a lot of things just by looking, you don't need an alignment rack to see things that are "off". Is there a lot of 'junk in the trunk"? Take it out. Make sure the battery is secure and all of the hold-down hardware is there. Once you can pass at least these rudimentary checks take the car out on the road. At low speeds you get what I call "blocking" at low speeds because the tires are so wide and cold. Kind of a rhythmic side-to-side leading. Goes away once you warm up the tires or go faster. To do the next checks you must find a flat, smooth, level road with NO crown. The car must go straight, the steering wheel must be level, and the car has equal turns to the left and to the right with no appreciable looseness in the steering. You should not hear of feel any clunking, banging, or shuddering even when applying brakes. The car should not lead or "pull" to either side when driving or braking. Again, you can't do this on a road that is not FLAT and SMOOTH. As mentioned you CANNOT align a car with bad, worn, bent missing parts. Well, actually you can but it will be worthless. The truth is most cars really don't need an alignment as much as they need worn parts replaced. Most of the time the parts can be replaced and that, by itself, will bring the car back into alignment. Keep the rubber covers (gaiters) in good shape, replace torn ones, lubricate and grease the front end and your car will last a long time and hold it's alignment.
Now on to alignments. If you want a good job and save some money, do some "homework". Get the car ready. Replace worn parts, tires, anything that needs attention. Do a service on the suspension (lubricate it). Have the correct air pressure in the tires. Note the position of the steering wheel and the # of turns each way. Remove everything from the car (not the spare). Have 1/2 tank of gas, the specs for the alignment, and a kit of shims. Ask if they will put weight in to duplicate the weight of the driver and how much (should be close to your weight). Tell the Tech any concerns or problems to look for like leading, understeer, oversteer, play, roughness, looseness, vibration, etc. Insist on a "4 wheel alignment". The rear is as important as the front, just not as complicated. Dealerships are not the best place to go unless they do that type of car all the time. Most dealerships are only good at what they sell, they don't get a lot of experience on other kinds of cars. Better to go to a shop that does all kinds of cars, they will have more experience doing "unusual" stuff.