Enroll in acting and singing courses --- whether in a 4-year college or a specialized arts institute --- to develop your craft. Get involved in the theater scene as much as possible, for instance, working in student productions and going out on auditions. Take acting night classes if you work during the day.
Get a professional head shot and accompany it with a well-formatted resume. List the roles you have previously played, as well as education and any special skills you may have --- hobbies, sports, dancing or singing experience and fluency in different languages. The more diverse your resume is, the better your chances of being recognized, as acting often demands diversity in its actors. Send this resume to casting offices in your town.
Try acting and singing in new media formats, such as Youtube. To stand out, you must be creative in these videos. Get friends together to create a web series to showcase your talent.
Develop a demo or acting reel, which is a video that assembles clips of your acting and singing talent. Get a talent agent. You can solicit your demo reel to an agent, or get a recommendation from a professional with whom you have worked in the entertainment industry.
Have realistic expectations and understand success will not happen overnight; even "overnight" success stories are years in the making. Stay focused and serious, and continue to develop our craft all the while. Also, make sure you love singing and acting as an art form, and that you are not solely in it for the fame and money. The latter group tends to burn out fast when these aspiring individuals realize how difficult it is to make it in show business and give up.