There are two methods of learning the information required for the certifications: being taught in a classroom environment, or through self-study. If you choose the class environment, such as through a course, then you should investigate your local colleges and see if they offer courses which teach for a specific certification (ie. a CompTIA A+ course). Whichever method you choose, you will need (or in the case of a course may be provided with) a book to study from. The book (should) be used as a "study guide". It is recommended when taking CompTIA certifications to obtain a book that has the CompTIA Authorized Quality Curriculum seal, such as Sybex's
CompTIA A+ Complete Study Guide (I highly recommend it).
To obtain the certification, you will need to take the certification exams at an authorized testing site, such as one provided by
Prometric (go to the website to find a testing site near you - to write an exam you may need to register). Once you've written all of the required certification exams and have passed, you will be awarded the certification. Depending on your location it will take some time, but eventually it will come in the mail in the form of a full-sized certificate and a wallet card (which, personally, I carry in my wallet at all times to show on the rare occasion that "Yes, I know what I'm talking about").
You may find when going to a major computer support/repair outlet that there may be a sign which states it is a
CompTIA A+ Authorized Service Center, which means at least half of its technical staff are A+ certified (or if it's a "Gold" center, then all of its staff). Call it a foundational standard - going to one means a customer can expect certain minimum standards in support.