Purchase a copy of the "Songwriter's Market." This guide may be the single most important reference you can have if you want to publish your instrumental music. The market guide is packed with music publishers and their guidelines for submitting your work. The guide features a section of instrumental publishers such as Hal Leonard and other publishers who publish instrumental music, including band arrangements.
Record a demo of your song. If you can't record a full version with a band, you can record a simple piano or guitar arrangement and send the full musical score with it. Consider spending money for studio time and at least a small group of instrumentalists. The more complete and professional your song sounds, the better chance you will have of finding a publisher.
Choose a couple of publishers that accept the type of instrumental music you want to publish. "Songwriter's Market" lists full submission guidelines and contact information, as well as the royalty structure for published music. Follow the guidelines of each individual publisher when submitting your songs.