You are going to have a hard time finding projects if you are in a company that has no UX projects or already has a experienced group of UX designers, so I suggest you do what many writers do in order to break into the TV industry – they write a "spec" script for a show that is already on the air, to show their writing and creative skill. Do that as a designer – identify a problem or a product that is sold in your preferred industry and design or redesign it.
Use a design process that works for you – I use a lot of techniques from Kim Goodwin's book – and document how you solved the problem. If your approach involves usability testing of potential designs, involve friends and family.
Build your design portfolio, and then look for entry-level UX jobs. Revise your resume to showcase your capabilities in design, not your experience. Attend conferences to learn new techniques, network with designers – and add the conferences to your resume, of course. And dont get discouraged if you dont get a job right away: keep trying!