With the exception of fuel, which I will get to, lodging can be the most expensive part of traveling if you don't plan appropriately; so plan appropriately. My recommendation is to camp as much as you can or a great suggestion from the about.com article is to use CouchSurfing, a site that allows you to find an open couch or room to stay in for free, with their mission being to spread cultural experiences through meeting new people. Campsites can be somewhat difficult to find, so you will want to look up sites along the way like KOA, which usually have showers and maybe even electricity if you are willing to pay. The most cost effective method though is to look up National Forests along the way, whose mission, according to the first Chief of the Forest Service Gifford Pinchot is," to provide the greatest amount of good for the greatest amount of people in the long run." They possess an astounding 193 million acres of land (the size of Texas), so you can rest assured knowing that you will have National Forest along your path and to contrast the National Parks, you can pretty much camp anywhere in a National Forest, just be on the lookout for hunters and dangerous wildlife.
As far as equipment is concerned, think of where you will be traveling/what time of year and ask yourself," What is the weather like along my route?" This means being prepared for rain, cold weather (even in the summer), and heat. My recommendation is to bring gear that is cross-functional, like a rain shell, which will keep you dry, stop the wind, and in the summer most likely will be good enough to keep you warm. If camping along the way, don't forget a rain cover for your tent and a change of shoes (or sandals/flip-flops which can double as shower shoes too). Making a list before you pack and checking things off as you put it in your car is the best way to go about preparing to ensure that nothing vital is forgotten.
The next step to preparation is planning for gas for your car. You hopefully have an idea just how many miles you can get on one tank of gas, but if you don't start figuring it out before you go on your trip, as it will come in handy to be able to estimate the distances you will be able to travel (make sure you underestimate because if you make extra stops or get caught in traffic you don't want to get stuck on the highway with no gas). Use either GoogleMaps or MapQuest to map out your planned route and take note of the larger towns and cities as those will be the best places to get gas (gas stations in the middle of nowhere are few and far between and usually more expensive to boot), stock up on food, and in many cases have some interesting history/sightseeing to do in or around the city.
One of the hardest things to do when Road Tripping is to eat healthy, especially with the myriad of fast-food options you will surely have on your route. The trick to avoiding the drive-thru is to get a decent size cooler and hit the Supermarket for snacks (think fruit, nuts, veggies, and trail mix is a favorite and great for energy), sandwich material (PB&J, meats, whole-wheat bread/pita, hummus, or whatever your favorite sandwich is), and dinner. Dinner is the best meal because you can buy plenty of supplies like meats, pasta, and sides that with a little preparation can be made into a meal you might eat at home. This will provide you with the fuel you need to stay alert and active while driving, sightseeing, and of course, enjoying your Road Trip.
Hopefully, after reading this and taking advantage of the hyperlinks in the article you will have a basic understanding of how to Road Trip with a budget and eat healthy along the way. Don't forget what the poet Robert Frost said about The Road Not Taken," Two roads diverged in a wood, and I---I took the one less traveled by, And that has made all the difference."
Here is a song to get you started Road Trippin'
Red Hot Chili Peppers