My house has two white wires, two black wires, one red wire and a ground wire. How do I connect my new fixture with one white and one black?

You didn't say if this is in a ceiling box or a switch box so Ill take it as if this is in a ceiling box.  The whites are your neutrals and the blacks should be power passing thru so connect white to the whites and the black from fixture to red,  and see if works off switch , if doesn't send me a message and Ill help you figure it out