Plan early in your education and academic career. This may sound strange, but Ivy League schools are much harder to get into than other colleges and often have an extensive waiting list to get in. You have to have extraordinary grades, school involvement, access to high tuition cost and career aspirations. Research the top 3 schools you would like to attend and learn everything you can about them and their acceptance process.
Consider college consulting services. If you are not a legacy or extremely qualified to get in, it may be worth looking into a consulting service to help you get in to the ivy league school of your choice. One such service is Ivy Success. They offer lots of help in many areas of getting you into Ivy League schools.
Plan for graduate school as soon as you start freshman year. Those coming from the school to the same college grad school have a better chance of getting in. Talk with your department adviser to plan for the admissions process when the time comes.
Go through the application process. Once you are ready, fill out and submit your application with all the required documents, fees and any other materials. Wait to hear back or follow up in a reasonable amount of time. The admissions office will be able to tell you how long to wait.