Get plenty of hands-on experience recording music. This doesn't mean you need access to mountains of expensive equipment in a state-of-the-art recording studio. Recording yourself and friends at home with a simple computer recording set-up or a stand-alone digital workstation will help you grasp the basic concepts of recording sound and help you develop the necessary critical listening skills.
Offer to man the soundboard for local performers at their shows. Most artists will jump at the chance of having someone fine tune the sound for their audience. As your skills develop, you can turn it into a paying gig, either as a freelancer or a house sound man at a live venue. Live sound engineering presents different challenges to studio work, but having experience with both disciplines will be beneficial to you as you break into the business, regardless of where you end up specializing.
Enroll in audio engineering classes. If your budget allows for full-time study you can pick a school that specializes in audio engineering degrees. If not, there are plenty of online audio courses that will help you learn the skills necessary to pursue a career in sound engineering. Neither of these options guarantee you employment in the field, but they will offer you the chance to learn valuable fundamental engineering techniques and become comfortable with the tools of the trade.
Network with professionals in the field. A good way to do this is by frequenting local venues and befriending musicians and their crews. Musicians and sound engineers generally love to "talk shop," so don't be shy about asking for tips and advice on mixing techniques, equipment and local employment opportunities.
Subscribe to an industry publication (see Resources for an example) so that you can keep up with developments in the industry and read product reviews. Recording systems and their software and hardware systems are continually being updated, and your continued familiarity with them is essential if you want to stay competitive in the field.
Apply for assistant positions at every recording studio in town. If there are no positions advertised, make it known that you're willing to volunteer your time. Working for nothing may be hard to swallow, but the experience you gain from being in a working studio will be worth its weight in gold, and if you prove yourself, compensation will follow.