How do I change my political party?

Re-register to vote, at your voter registration site.

Or, just vote in opposition of the party you are currently registered as?

You can vote as you please, without regard as to how you are registered, changing it on your voter registration is only a formality.

Some states permit you to register as an Independent outside of the two major parties. In Nevada that's how I'm registered. But like Progunr mention it really doesn't matter how you registered, you still are permited to vote as you choose. But do make sure you are registered, especially if you have moved without providing notification to receive a new registration card, usually sent by mail within 7-10 days.

In most states you can contact your county board of elections to get an application . If you tell me the State and county you are in I can probably get you a downloadable application .