You don't need a particular education background, although you CAN get a technical writing certificate or degree. I dont have one, but I learned a lot about my field. I worked on a helpdesk, and my 'notes' that I made for myself turned into a training manual. after that I worked on several other projects and eventually got promoted to a documentation specialist.
What you really need is to search out opportunities in your company. Show interest and if you have anything already documented, share that. Just be ready to stand up for why you should be doing the documentation and be willing to learn learn learn.