To start out your career in travel photography you are going to start as you would with any photography career, by getting education, developing a portfolio, and making contacts. Photography school is a good way to begin, but most importantly you will need to intern in comparable publications, such as travel magazines or even the Travel Channel, and do photo series' that show off your skills in representing locations, cultures, and characters. What is going to be important during these early points is to learn other languages to assist your goals, as well as cultural institutions and how the general practices of business work.
Do not start incurring costs right off the bat as you will not have income coming in. Instead, begin creating travel portfolio elements from locations that are nearby or places that you are traveling to for other reasons. Travel photography does not universally mean locations that are far away from you because that is a relative term to an international audience. Instead, a good travel photographer will just draw out the beauty and individuality of a place. This can be done in your own community even, as long as you find a way to create high quality images that hold a lot of character and visual production value.
You can begin doing your own travel missions along with it, but you will have to note that you will have to cover these costs yourself. The best way to do this is to find some publications ahead of time that may be interested in what you are doing, so it is best if you have a unique take on some travel idea. For example, you could propose that you do a backpacking tour of eastern Europe and you send this idea over to magazines that deal with youth travel, Eastern bloc countries, Cold War architecture, and the like. What you can expect is to sell photos to several locations from a single trip, each in a different context.