I don't.
That's the simple answer.
I do not know if I'm an awesome writer. No one does (except maybe Carrie Ryan, but I'd bet she has her off days too).
Writers are plagued by self-doubt. I don't know if it's just part of the artist personality, but we are. I don't know one writer who thinks she's (or he's) the shit twenty-four hours a day.
It's this fear that paralyzes many writers, whether they are seeking an agent, releasing their third New York Times Bestseller, or jumping into the indie pool for the first time.
What are the best ways to combat this fear?
Chain smoking at the nearest park? Drinking yourself into oblivion? Whining about how everyone else sucks because they can't see how fantastic you are?
Um, no.
You combat this fear by working your ass off. Go to workshops and conferences. Take classes. Attend critique groups. Write, write, write, and write. Be open to new ideas. Have your work critiqued by professionals and your peers. Don't publish your first novel the day after you finish writing it!!!!
Like any other successful career, writing takes hard work, determination, and indomitable spirit.
Keep this tidbit in mind too: Jane Yolen has written and published more than 300 books, won countless literary awards, and has six honorary doctorates in literature. Guess what I learned by being Facebook friends with her? This woman is probably the most legit writer in contemporary children's literature and she still gets rejected occasionally.
Rejection happens. Move on and become the very best writer you can be!