Take classes on theater or film props in school. It is important for a prop designer to be knowledgeable on how to make basic props. Further your education in a professional setting by finding an internship or apprenticeship that will allow you to observe and assist a prop designer either on a specific film or with a company that specializes in prop design.
Contact a film school near you or the film department of the school you attend and let them know that you're interested in working on props. Start by working on student films, since they often seek people to help out who might not have experience but who are eager to learn and sometimes willing to work without pay. One benefit of working on a low-budget film is that it will force you to get creative regarding how you fabricate props and how you spend within your budget.
Be a hard worker who shows up on time and contributes thoughtfully. Listen to what the director wants. Be sensitive to anything special that the actors and other designers need from you. Treat yourself like a professional so others will react to you as such. Like any position in the entertainment industry, word of mouth is a crucial factor in moving up. Don't be afraid to introduce yourself to the other people on the production team. The more people you get to know, the more future projects that are likely to come your way.
Start as a production assistant, or P.A., on a professional film set if you're interested in working on a larger-scale production. Make yourself available to designers on set and share your desire to work with the prop master.