How much research experience or publications are required to get into a good PhD program in USA
I think you should focus more on the quality and focus of your research than the amount. If you are researching a concrete topic, and have 1-2 solid works dealing with it, then you are golden. Make sure you explain the value of these works in your research statement/essay. That would be more or just as important as the resume, because it is an expression of you as an individual.

Other people will tell to go down the bullshit path and sprout several pieces that milk the same research but add little to the field. Some schools will buy that, but others will not differentiate you from the rest of students. You can also try this approach, but it may be even more time-consuming than the first.

Reading your question again, it is better that you engage in research before applying. Perhaps you can contact a professor and work with him, or a PhD student at your university, or find a research institute in which you can put in some time.