@Jakebeal has given you one very good option. If you can do this, and it won't take up too much of your time, then you probably should.
Alternatively, if you have no possibilities for joining a research lab, or you need more personal time that that would allow, another option which you might consider is collaborating with a researcher to write a literature review paper in an area that you are interested in.
Before doing this you would need to i) identify what to do with the paper (even publishing it on a blog could work) and ii) someone with publishing experience to collaborate with when doing it.
You need i) and ii) resolved to make this work, but both are doable. For instance you could email, or visit researchers, and ask them to i) suggest a place you could submit a review to, and ii) to supervise you with it.
The benefits (relative to working in a lab) are that this would be less time consuming and freedom restricting (you could work on it when you wanted). You could therefore have a non research job, take a holiday or do whatever. You would still be able to potentially get a reference and would definitely get some research experience. Of course the tradeoff is that you would not gain as much as if you actually worked within a laboratory, or directly within a research team.
Please let me know if you would like any more details/suggestions related to this :)