All countries have some sort of selection process and I suppose in some you could just show up at an open tryout, but more likely the best athletes will be invited to compete. You can't just show up in Bejing and tell the officials you want to enter an event.
Chat with our AI personalities
The modern Olympic Games is a competition between countries rather than individual people. Whilst most of the actual events are between individuals, there are a few, such as rowing events, which comprise teams rather than individuals.
But people can only enter the Olympics if chosen by a participating country.
Note that many of the participants aren't countries. My understanding is that some people prefer independence from the rest of their country; athletes can compete independently (e.g. Yugoslavia in the last century). I think you would apply to the Olympic Committee to have your own team.
Those countries that have a National Olympic Committee are eligible to participate in the Olympics.