Honors and awards can help, but are not necessary.
The easiest way of getting into even big universities is if you know the mantra of getting funding. If you can get money universities will hire you. This is the biggest consideration, other things are secondary.
Most universities in US don't care whether you are international or not, so this answer is equally applicable to US citizens.
I like to blog about various topics ranging from education in IITs to social issues in India and US. All opinions and views presented here are my own and not of my employer.