From a Canadian perspective of your country:
The right would consist of those who favour small government, de-centralized government (ie. State Rights,) tax cuts, a strong military, strong law and order, markets free from government interference, unilateral U.S. sovereignty, and traditional family values, with a dash of Christianity thrown in, pro-business, privatization.
The left would favour social programs, a strong federal government, progressive taxation (ie. tax the rich, give to the poor,) other spending priorities sometimes higher than the military, a rehabilitative justice system, regulation of buisnesses for the greater good, internationalism, liberal secular values, multiculturalism, pro-labour, nationlization.
Of course, you can find both Democratic and Republican compromises on all those topics.
The center would be a moderate position on all those values. Limited regulation,only for important stuff; federalism over state rights in some cases; some welfare, but not a huge amount of wealth transfer between the classes; a strong military, but not spending too much money on it; a justice system that tries to rehabilitate, but keeps in mind punishment. Probably a pragmatic approach to international affairs. Probably saying as little as possible on moral issues, too many people think they are black and white.
It's a hard thing to pin down, partly because the pendulum is always swinging between the two sides.
Hope that helped.