When renting a car in the US you need to be at least 21 years old with a valid drivers license - if you're from outside the US your country's driving license will be fine, there's no need for an International driver's license. Although you may be 21 years old that's not to say that every rental company is obliged to rent to you - some rental companies have a 25 year minimum age or require an additional payment if you're between 21 and 25 years old - prices vary so shop around. Most companies will also require you to produce a credit card before leasing you a vehicle.
Also, don't forget that most hire cars in the US will be an automatic transmission so if you want to drive a stick shift be prepared to pay extra!
Inform your rental company if there will be multiple drivers prior to signing your contract and budget for an additional payment for the privilege - this varies between companies - be sure to check on this.
There are several major companies to choose from when renting a car:
However, trawling through each of these sites individually, having to enter the same information time and time again soon becomes tiresome. There are websites out there that will search all of these companies on your behalf to find you the best deal. If you don't want to spend the time searching each company I would recommend using RentalCars.com - a price comparison site that will do all the donkey-work in finding the cheapest deal.
I have always used this company to help me find the cheapest deals for car rental and have never been disappointed - they are easy to communicate with via email or phone. One point worth noting is that if you get an estimate for car hire online but do not book straight away, they often wait a couple of weeks before sending you an email with a slightly reduced rate to entice you back!
When renting your vehicle be sure to understand that you are responsible for any damage to the vehicle and that you'll be presented with several insurance options by the rental company. At the very least you will need liability insurance to cover any damage caused to third party vehicles but I'd recommend a comprehensive insurance in order to cover any damage to your own vehicle too. A great tip is to ensure you take out any relevant insurances at the point of booking - if you try to sort this later, when picking up your vehicle for example, you'll almost certainly end up paying more.
Some credit cards, such as American Express, will offer rental insurance if the card is used to pay for the rental but be sure to check this in advance and if needs be ensure you're not being billed for separate insurance by the rental company.
Of course, your insurance requirements will vary depending on whether you're booking from within the US or not...
Disclaimer: Obviously this advice can't cover all eventualities and insurance can be minefield. The advice given here is consistent with most of the large rental companies but always check your policy details.
Most rental companies have locations at airports, large hotels and cities and are plentiful across the US. If none of these locations are suitable for you then Enterprise offer a service whereby they will come to you when you are ready to rent your vehicle. Whichever you choose just make sure you have your passport, driving license and credit card when you collect your vehicle.
When you book your car you will most likely only be able to specify the type of car (compact, saloon, 4WD, sports, etc...) rather than the specific model. Upon arrival at your chosen pick-up point you will likely be directed to the area of the parking lot which houses your type of vehicle and you will be able to choose your own vehicle from the available selection - a very exciting experience!
Once you've picked out your vehicle be sure to give it the once over and check for any damage to bodywork no matter how small. Bring any dents, scrapes or paint chips to the attention of the rental company so that they can document it - you may want to take a few photos/videos yourself for peace of mind.
In the unlikely event that you should encounter a problem with your car, most companies will either repair the vehicle if it's unable to start or more likely replace the vehicle if you are able to get it to the nearest branch (which are numerous and widespread).
Most cars in the United States are fitted with an automatic transmission and will only have two pedals. If you are used to a manual transmission then you can forget the clutch - your car will only have accelerator and brake pedals. With an automatic gearbox you set it to P in order to park or stop, D to drive, and R to reverse. It can take some getting used to but makes for a very easy driving experience.
Before hitting the road be sure to take a few minutes to familiarise yourself with the essentials such as turn signals/indicators, high beam lights, wiper controls and AC settings.
Your car will be presented to you with a full tank of gas and you will be expected to return it in a similar state. If you return the vehicle with less gas than you started with, the company will fill it up to the desired level for you but will charge a premium for this (sometimes as much as twice the cost of having done it yourself!)
Most people that drive Route 66 opt to return their car at alternative site to where they collected it. If you wish to only use your vehicle for a one-way journey (Chicago to LA or vice versa) then you will have to pay a one-way drop-off fee. Be sure to enquire about this with your chosen company as it can vary from company to company. Alternatively, if you're booking your car hire through RentalCars.com then this is taken into account when providing you with your quote.
Just as you gave the car the once over for bodywork damage when picking it up, be sure to do the same at drop-off. I always take a few photos of the exterior of the car when dropping off as a record of the condition I returned it in.
I hope this information has been helpful - enjoy your trip!