Can you apply online for a grant?

Absolutely!  A lot of the organizations that have grant programs also have websites that let you either download their application or let you fill out the application online and submit via their website.

Would it also surprise you to know that some of these organizations provide email addresses so that you can contact them for more information?

But don't forget about the organizations that aren't online yet.  They still have phone numbers and regular "snail" mail addresses too.