Applying to graduate school is a stressful time in the lives of most students. These days, it seems like fewer and fewer good jobs are available to people without graduate degrees and, as a result, more and more students are competing to get into the best graduate programs. Attempting to distinguish yourself from the hundreds of other applicants to most graduate schools can be a daunting task. Make sure that your application is as strong as possible, and do not wait until the last second to turn it in.
Whether you are applying to law school, business school, medical school, or some program in the humanities, you are going to need at least a Bachelor's and in some cases a Master's degree first. No graduate school will accept a student who has never actually graduated from college. Most programs will allow you to apply while you are finishing up your last year of college, since most applications are due in October or November for programs which start the following September. Depending upon the program you are applying to, you may need a degree or at least a significant amount of coursework in a specific field.
What type of standardized test you must take will depend on what program you apply to. For medical school, you will be taking the MCATs. Law students take the LSATs and applicants to all sorts of other programs take the GREs. You need to consult the program you are applying to in order to find out exactly which test they require. You need to plan way ahead, since most of these tests are only offered a few times per year and you will probably need to spend at least one year studying for your particular test.
Your statement of purpose is the document in which you explain why you want to go to graduate school. This document is one of the most confusing parts of the application for many college students. That essay you wrote about how your grandfather inspired you to try out for the football team that you submitted with your college application isn't going to cut it, and you can forget about writing about your personal or spiritual development. Graduate schools train professionals. Admission committees want to know exactly what you want to study, and how your research is going to contribute to the field you enter.
If you are applying to a top tier program, especially in the humanities, your letters of recommendation could be the most important component of your application. Often, these letters are what distinguish one undergrad with a 4.0 GPA from 100 others with the same qualifications. Instead of asking your favorite professors for letters, ask the professors most famous in the field.
Lots of graduate schools won't require that you interview before you apply, but it is a good idea. If the faculty of a graduate program is willing to meet with you in person, you have an opportunity to impress future professors and make yourself stand out from the crowd. Interviews are also a great way for you to get a feel for your potential advisors' personalities and mentoring styles.