How to become an olympian?

1. Eat a balanced healthy diet. Avoid too much fried food and sweets. As a vegan, you already know that you need to plan carefully to get enough protein. You also need to eat a lot of foods rich in iron, since iron from plant sources doesn't absorb as well as animal sources. And also make sure you get enough calcium and vitamin D, dairy is the most readily available source, so again, you have to plan out your eating to compensate.
2. Since you're 16 (per a previous question), you should be running track (and also cross country if you have time in the fall). That should require running 6 days per week with the team. During the off season, you'll likely be running 4 or 5 days per week. Olympians often train longer cycles, 8 or 9 days on, 1 day off. During any given week of training though, you'll have a mix of hard training and easy miles.
3. You can easily find 800m training schedules online for any experience level. Some days will be easy, no more than a light jog to improve cardio and put mileage on your legs. Some will be very hard, short repeated intervals at race pace or tempo runs that are longer and slightly slower than race pace. There are many different approaches.
4. In 4 years, not likely. Very few elite runners come forward at the Olympic level by age 20.

There is a normal progression, unless you're a unique talent who surfaces at a young age, you're likely going to follow this progression. Run for your school. Work hard, and if you have the talent and perform well enough, you'll have the opportunity to run in college. If you perform well enough in college, opportunities to compete at a higher level will become available.

The best advice I can give you is write out a list of questions and go to an athletic club and ask a professional about joining, basically just ask them what you asked here. This is the type of question where you are better off hearing from someone in the athletic industry.

You do Exceptionally well in school sports.
The Coach or News Media recommend you to the Olympic committee
A "Scout" views your activity.
And, if you show promise you get hired.

The Olympics is no longer the Amateur Group that it once was, where the store clerk worked out evenings, and weekends and anyone could apply for entry.
It is now a bought and paid for Daily Employment sponsored by the Government elitist group by invitation only. If you don't make it here you immigrate to another country if they show interest.

Okay, first off you need to completely revamp your diet and train everyday except Sunday.. Use that as a weight lifting day but a light one at that just to keep muscles moving. Train with resistance bands and body weight workouts. Shred your shoulders until you can literally see your muscle fibers through your skin. The faster you can move your arms the faster your legs will move, it's just the way to body tricks the mind past a barrier when it comes to running. Hydrate, hydrate, hydrate! You need to drink twice your body weight in ounces of water a day for the amount of training you need to do to become an Olympic athlete. For example, if you weigh 150 drink 300oz of water a day. You should start running around 30 miles a week and gradually bumping that up to around 80 a week. The higher you can go the more it will benefit you. Just remember you will be training to compete against the best runners in the entire world. You're more than capable, everything you need is within you!

practice, practice and practice.

If your PB is 3:03 in competition, there is no way you have done it under 2 minutes. As an 11 year old school kid in PE I did it in 2:36 and I'm not even that athletic. Nobody drops over a minute in competition for a race as short as half a mile

Vegans cant go to olympics due to their severe vaginitus.