Get your math skills in order and pay specific attention to complex concepts involved in topography, such as notions of completeness, compactness and separation axioms. You should have a very strong grasp of Cartesian and Euclidean geometry and the lexicon involved in these two fields of math. You also need to understand basic terms and concepts from homology (including basics of abelian groups) and homotopy theory.
Take a look at Allen Hatcher's comprehensive study on the topic, entitled "Algebraic Topology." Hatcher's book, which is widely considered to be one of the "bibles" for the study of algebraic topology, is available online for free download, making it a very good opportunity for you to peruse the text to see what you need to brush up on before diving more deeply into the topic.
Study algebraic topology by making use of the MIT's Open CourseWare program that allows you to follow along with the MIT version of the course for free. Try to do all the reading and assignments that are prescribed by the MIT math department's version of the course so you can get the closest thing as possible to a comprehensive course in algebraic topology.
Enroll in a course at a college or university that offers an introduction to the prerequisites for the course and then takes you through an entire class dedicated to algebraic topology. Make sure that the college or university offers follow up or advanced level courses in the field so you can continue to study and make good on the initial work you put into learning this math topic.