How would I make a search view display results in a new page instead of on the same page?
You can show your exposed views filter as a block, and place the block on your search page, then all submissions will show results on your view page.

Under the advanced field-set in the views UI, once you have created an exposed filter, an option will appear under the EXPOSED FORM heading that will allow you to create a block.

You can see an example of a front page search leading to a views results page here... http://www.myweddingfayre.com