Well the obvious answer is grad school. The second answer is to become what many call a junior specialist..a paid researcher.
This. And a graduate degree is often a prerequisite for research positions in the private sector.
I'm sure it depends on the field, but volunteering as an unpaid intern can certainly get you in the door. It's a good way to get experience and contacts that will help you get into grad school. You also get to see the research process and get a sense for how much you like it, or not.
There are a lot of companies that work in research. Look into the National Labs. Look into DARPA and NSF funded groups. Also most research universities hire non students as well. This can double is a way to bootstrap yourself into grad school