Assuming you are buying from a dealership:
#1 Don't get emotional over any part of the process. If the numbers don't work, you'll find something else. If you remain calm knowing that you are in charge and you don't have to buy, everything will turn out ok. You should be in no hurry
#2 Run a loan calculator to see how much you want to spend. If you have a trade, go to KBB to get an idea of what it's worth(be honest on condition) and do the math. As an example, if your trade in is paid off and worth $5k, you don't want your payment to be over $350/month for 3 years then you have $12k plus your trade, so you should be looking at cars for around $17k. TTL will probably be around $1k so put your limit around $16k.
#3 Go to cars.com, autotrader.com, and carmax.com. Put in criteria i.e. sedans, less than 40k miles, maximum price of $16k, a few makes (Honda, Dodge, etc). See what comes up and pick out a few models that interest you.
#4 Get pre approved for a car loan. You don't have to get the car loan at the place you get pre-approved but it's good to have to give you an idea.
#5 Go test drive some of these cars. If asked (you'll be asked) , be honest and say "I've just started looking and this is one of the 3 models I'm considering. I'm not buying any until I drive all 3". No matter what they say after this it doesn't matter because you are in charge and are going to walk out the door when you finish. Grab your salesman's info and keep it. Tell him you'll hear from him in the next few days after you get a chance to look at the other 2. They may tell you that "This may not be here tomorrow", "This deal is only for today", "Let me talk to my boss", etc. None of this matters, walk out the door.
#6 Go home and figure out which model you like the best. Do research on forums for that model, which will give you a good idea on known issues with certain models/years. If you find one that you really like run a carfax on it. Again look online and see if there are similar models locally that you like.
#7 Once you've picked out a car, email the sales person and tell them you want to know what the best deal they can give you. Tell them you need to know the bottom dollar (not monthly payment) and whatever number they give you you'll consider it their best offer so that you can compare it to another that you're considering. Do your best to not go back in unless you're ready to pull the trigger.
#8 See how the numbers compare and then when you think you have a decent deal email them and say "If you come down to $****, I'll buy today". They will probably meet you somewhere in the middle and that's ok. Don't lose sleep over a few hundred. I've heard of people spending 6+ hours fighting with sales guys over a few hundred, it's just stupid.
#9 Get the final number including TTL in writing. When it comes to financing, they may want to offer you a loan and that's ok. Just compare it to what you got pre-approved. Don't fall for any extras, if you buy a good reliable car, you don't need a warranty.
On a side note, if you buy from carmax, you can skip a lot of these steps but you may end up paying a little more. It may be worth it to not go through what some people consider a hassle.
I think people go into the car buying process with the wrong attitude and they usually crack from the stress. Look at it as a fun experience where you are the one in total control. Have fun with the process, you're the one getting a new-to-you car.
On a side note, it would be good to give us your budget and maybe we can help you pick one out
addressing the single most critical feature of your next car? I am here (again) to preach the gospel of COLOR! Nothing is more important than picking a car with a cool color. If the color itself doesn't wow you than the cool name of the color should, like Ocean Blue Pearl Effect, British Racing Green, Metallic Meridian, etc.