The trick is to be able to say it, mean it and shirk off any disapproving responses from those around you. Presume they are jealous that you are good at something they shall never be.
Saying you are awesome is fine as long as you can justify it. Sometimes, as in a first introduction to new people, it does nothing but cause uncomfortable silences. In some (frankly) it actually pisses me off. Because you can't just say you're awesome for awesome's sake You have to be genuinely good at something or just win at life. Because being good at life is a skill in itself.
I'm not sure I'm comfortable with settling myself into the awesome category yet. In what I do I have skill but there are others far better and far more ground breaking and I won't deny I have my faults and have made my share of cockups in life. I don't win at life. Although I suppose the fact I am still here and relatively sane makes me a winner.
I guess there's always someone better than you at something. Within my immediate circles I am hitting a certain standard but out there in the wider world I am a very, very small fish in a very big ocean. I have a long way to go and I am very much aware of that. But at least I had the balls to start somewhere.
You should always strive to be better at what you do, better read, more worldly, more interesting. Whatever it is that makes you just that little bit more awesome. So be awesome.