Second, Get one of any number of textbooks on basic calculus. They usually say "Calculus" in big friendly letters on the front. You can buy one for around $100, or better yet, repeatedly borrow one from your local library.
Spend anywhere from a month to a year working through the textbook, depending on your free time and motivation. This means reading and re-reading the material, section by section, and convincing yourself of the reasoning and proofs laid out. However, take a healthy skepticism toward each argument until you can "see" it for yourself. Even math texts contain typos and flawed reasoning from time to time.
Last, take an hour or two a day to do problems. A good technique for an armchair mathematician who is really only concerned with being acquainted with calculus (as opposed to mastering it) is to give a problem your best shot, and then check the back of the book. Since only the final answer is usually given, you can use this as a guide to correct any bad reasoning, without having someone hold your hand. Go back and rework your problems.
If you can do these steps, you will be acquainted with calculus.
Differentiation and integration are deeply related.