One of the best places to gain valuable experience is online. Social media has become a huge venue for media professionals to share, collaborate and find work. This sharing has created a fantastic resource for students and amateurs to learn and study from. Look online and you can always find some creative that has shared their own technique or style that you can incorporate into your own work.
Here are a few links highlighting how easy it is to find information that you can apply to your work. The first is a tutorial on how to set lighting for a commercial photo shoot and the second is how to set your DSLR camera to properly capture HD video. The information is out there at your fingertips, you just need to look for it. Search Twitter feeds, add blog sites to your bookmarks and use sites like YouTube and Vimeo as constant resources.
As far as hands on experience, my suggestion is to make yourself more valuable. Shoot more photos and video and then shoot some more. Learn about and perfect your professional etiquette. Understand the technology that you're working with and how to use it properly. These are just a few things that will make you more valuable the next time you're trying to find work as a production assistant. Check out the blog post from professional photographer @BlairBunting where he shares what he looks for in an assistant. Read it and then try to apply it to yourself the next time you're asking..."where can I get more experience?"