It is not always possible to go with your car to a foreign destination. This is because of logistical issues, cost considerations, and time considerations. If you do not intend to be driven around in a taxi in the foreign country, you should rent a car. The advantages of renting a car in a foreign country are that you will pay less compared to renting a taxi, there is convenience compared to taking public transport, and you get to travel to places where public transport would not take you. Different countries have different rules when it comes to visitors renting cars, but there are some general rules that apply to all countries. You will need an IDL or an international driver license in most countries. However, your American license will be accepted in western European countries and several other countries. Do research on the country to see what is acceptable. You can get the IDL from your local AAA offices.
Note that your automobile insurance policy may not be valid. You should check the limitations and restrictions. All this information is found on the fine print. If the insurance is not valid in a foreign country, you can get coverage with your insurance company or in the foreign country. Your license will be taken if you are involved in an accident or if you are involved in a driving violation. The license will not be returned to you until you have paid up. You should therefore carry enough money because of these and other charges. You may be mistreated in some countries after an accident and in such a case, report to your embassy. In most countries, especially the European countries, you will be asked to pay for any fines that that the car rental company gets from the authorities because of your traffic violations. You should therefore be careful while driving because there are many street cameras on intersections that photograph cars that violate traffic rules.
Your travel agency can help you with your car rental. You should contact the agency way before the travel date with details on the period you want the car and the type of car. This will give them ample time to get the car. You can make reservation online with car rental agencies, which will require you to make a deposit with them. Try to bargain as much as possible - you have nothing to lose. To get the best possible company at the best possible rates, compare as many car rental agencies as you can. The internet is the best place to do this since there are hundreds of car rental companies to choose from in each country. Review the street signs and the traffic rules of the country you are visiting. Some of the rules are very different from American rules, such as keeping left unless overtaking. Organize with the car rental company about where you will pick up the car and where you will drop it off. You can drop off the vehicle at a location different from where you picked it, at a fee.