Student Travel Association (STA) is a good source for reduced fare tickets, as well as Student Universe or Travel Zoo. If you are using a student fare website, you can expect that they will ask you for your International Student ID Card (ISIC) number when purchasing the fare. We sell the ISIC card at a cost of $22 p/card. Visit OSA for more information regarding this card. Don't forget to search any of the non-student fare discount sites, such as Travelocity, Orbitz, Expedia, and Kayak. Be careful that you do not schedule layovers that are too short to catch a connecting flight and also be aware of all restrictions (non-refundable, non-transferable, etc.) on a particular ticket. With increase airport security measures, check in for any international flight at least 2 or 3 hours ahead of flight time.
Discount airlines in Europe now provide inexpensive and timely ways to travel long distance for a number of smaller airports throughout Europe. Some examples of these discount airlines are Ryan Air and Easy Jet. Do keep in mind that different luggage restrictions apply to these airlines, so you will be limited in what you can take with you without having to pay steep fines.
Check Rail Europe to find out all you need to know about train travel in Western Europe. The Eurail Select Pass can be an outstanding deal, but make sure that you are going to travel enough within qualifying periods to justify the cost. The Eurail Pass is a cost savings if you are planning to travel long disctances (more than 4 hrs) for a number of times. The Eurrail Pass must be purchased while you are still in the U.S., and may not be used in the United Kingdom or in most East European countries. Students normally buy 2nd class passes, which is fine in Western Europe. For some trains there may be a need to reserve seats in advance. There is a nominal charge for this. Also see Dan Youra's Ferry Guide for information on European railway and ferry systems.
Renting cars in Europe is more expensive than in the US and may have different age requirements than in the U.S. Also realize that traffic signs and regulations can vary greatly (think about driving on the left side of the road in the U.K.). Traffic accidents account for the majority of injuries and deaths among students abroad. Rather learn how to use local buses and subways. In your city of residence you can probably get monthly passes. Even for shorther stays buying tickets in bulk, i.e. ten Paris Metro tickets, the Paris one-day or three-day pass, or London one-day travel card are often available at reduced prices.
Youth hostels are still the 1st choice of students to see Europe inexpensively. In fact, hostels are available in many countries outside of Europe as well. For information visit the International Youth Hostel Foundation, or do an on-line search for Youth Hostels.
Absolutely learn about your host country before you go there. Get your hands on travel books, such as the "Let's Go Europe". If you are going to travel more intensively in a particular coutnry, there are volumes in the Let's Go...series for several major countries, i.e. Let's Go Europe combines about 10 popular Western European countries. Also recommended travel books are the Real Guide, and the Berkely Guide Series. For Asia and third world travel, the Lonely Planet series is the usual choice. Also visit on-line the Froghouse for student listed recommendations for travel etc.