The word right has several meanings:

1. Correct or true. When your answer on a math problem is right, you've solved it accurately. When someone says “you're right about that,” they're agreeing with you. The right way to spell a word is the correct way. This is the opposite of wrong.
2. A direction, the opposite of left. If you're facing north, east is to your right. When giving directions, you might tell someone to “turn right at the corner.” Many people write with their right hand, though some use their left. A right turn usually goes clockwise.
3. Something you're morally or legally entitled to. In America, citizens have the right to free speech, meaning the government can't punish them for expressing their opinions. Kids have the right to be treated fairly by adults. These aren't privileges someone can give or take away: they're fundamental to being human or being a citizen. When you stand up for your rights, you're insisting on being treated as you deserve.
4. To correct or fix something. When a boat tips over and then rights itself, it returns to its proper position. You might try to right a wrong by apologizing and making amends.

The phrase “right away” means immediately, while “right now” means at this very moment.