New York Times Crossword

[PBAR]

I started doing crossword puzzles from the newspaper a couple years ago. I recently moved and the newspaper in my town prints the New York Times crossword. After Wednesday I don't have much hope in doing it. When I look at the Sunday puzzle, I always wonder, who can actually do this? Are there OOTers who can solve the Sunday puzzle without assistance (ie Google). Were you always able to do it or did it just come with time? I think age plays a large role (I'm 23), how old are the people who can solve it? Also, how beneficial is it to fill in blanks once the solution is received? Any tips would also be appreciated.