1. You have to be really smart, but not THAT smart, just smart enough. Don't worry so much about being academically perfect, but just be really good (C.G.P.A > 3.7 /4.0 )
2. Don't worry about the GREs, plan ahead and do them when you can focus, but don't worry about the scores. If you're aiming for a top Ph.D. program, most likely it's in your blood to do the best you can on any test, so I know I can't stop you from studying really hard, but just don't stress too much.
3. Look at schools and programs early. You have to apply at the beginning of 4th year before you do anything, meaning that 3rd year is really important. So start looking at schools between 2nd and 3rd year. You want to tailor what you do in 3rd year towards the short list of schools you want to get into (i.e. match interests, pick courses that are applicable to the programs you're interested in)
4. Do research VERY early. During first year start talking to your professors about what they do. Do research with them during the year or in the summer. Volunteer! don't expect to be paid, getting a paper published will be worth a lot for you in terms of grad scholarships, etc... In second year, start getting to know the research groups in areas that interest you and sit in on weekly meetings. Find projects you're NATURALLY interested in and ask if you can help out grad students working on those projects. Basically, do anything you can to get as much exposure as possible without wasting professor's time.
5. Before third year, talk to a professor in a field you're interested in and ask them what the top schools in that area are. Start learning the names of professors at those schools that someday you might work with.
6. If you don't have a thesis or undergraduate project in 4th year, find yourself a professor who wants to be your advisor. Ask if you can have weekly or biweekly meetings just to talk about the area of research, people in the field, and ideally work on projects with them.
7. Don't email professors from other schools. Some people say it's a good idea around application time, I don't think it is. There's a lot that goes on behind the scenes, professors know each other and if you follow step 6, your advisor will tell the other profs about you and things will magically work out. Let your advisor talk for you, they hold 10000x more influence than you do.
8. Look into the administrative details when looking for schools. U.S. schools are expensive so look for programs that have full funding. Look at where the graduates go and where the current students are from. All schools tell you how great they are, so look for objective facts that show in which way they are great. Do they get a lot of publications? Have top facutly? Produce students who go to top schools? Have current students from top schools?
9. Find what you really like to do. Don't be swayed but what people tell you they think you should do. Don't be swayed by what things SOUND like. What you learn in school is stuff from many, many years ago so look at what people are doing NOW. Look for conferences that sound interesting and look at the researchers who publish there, then look at the schools they're from and the departments they're in.
10. Apply and then wait, March of you're final year will be the busiest month of your life so far, I promise... that's when acceptances come in and you fly all over the place to meet people.