The most challenging task facing college transfer students is the transfer of credits to the new school. Often, students transferring from a two-year college to a four-year university will be required to take some classes over to fulfill the new school's prerequisites. Moreover, some schools are on the quarterly system, while others are on semester systems, which can complicate the process of getting credit for the courses you have already completed at your current school. In addition, the new school might not have a particular course or major that is equivalent to those offered by your current school. For all of these reasons, you should contact your new school well ahead of your transfer so you can find out exactly how many credits you will receive and which courses you will be credited for.
Transferring to a new university works the same way as applying to a new college for the first time. Ideally, it should be done far in advance of fall semester (or the first quarter, if the school is on a quarterly academic schedule). Schools will usually tell you on their websites their transfer application cutoff dates and what materials you will need to send in to them. This will likely include letters of recommendation and a copy of your official college transcript, which must be sent by your current school, sealed and postmarked to ensure no grades or credits have been forged or altered.
Many schools also require an essay on a topic of their choosing, to demonstrate your ability to structure and write a college-level essay.
Getting to know a new university can be difficult, which is why schools typically have orientation programs for newly enrolling freshman. As a transfer student, you are eligible--and would be wise--to attend freshman orientation and/or take an official campus tour, in order to more intimately acquaint yourself with your new school's history, culture, and campus layout. (Most schools also have maps of their campuses available at the main administration building.) If you will be attending a college outside of your current city, you would be well-advised to visit that city beforehand, to investigate both the school and the off-campus environment, and perhaps decide on where you would like to live.