Studying abroad is a great opportunity to learn about different cultures and explore new places. College is a rare opportunity where travel to new places for an extended period of time (semester or even a year) without having to consider life responsibilities (works, bills, etc) that later in life make it hard to travel.
You should talk to your academic advisor and the study abroad office. Start early so you can plan in advance. There are ways to tailor your study abroad experience such that credits taken abroad count towards you major and won't hinder your academic progress. Additionally, your school will have partnered study abroad programs. This programs have similar costs structure similar to your current tuition and room and board structure. From a financial point of view, you would pay for the study abroad program the same way you do currently, usually directly to the school bursar's office.
When you are abroad there will incidental costs (eating out, transportation, and personal care) that you'll need to budget for and plan ahead for. I worked the summer previous to when I studied abroad and saved all the money I could to cover incidental costs. Also check to see if there any scholarships for studying abroad and apply for them. I had an additional 2k in scholarship funding to cover costs of books and materials directly from my study abroad program based on my grades and course of study.
Good luck and I hope you get the opportunity to travel and have new adventures.