How can I start building relationships with people I admire?

Social media in the 21st century can be a blessing or a curse, in this case it's certainly a blessing. 

For the time being, how about start following these people on social media, learn about their hobbies and interests. Perhaps reach out via direct messages.

Of course respect people's privacy and don't spam them. But it's a good way to start. The other thing you can begin doing is go to places these people usually hang out and when you gain more confidence you can approach them. Who knows they just might approach you!