Musicians are sponsored by a variety of companies in several different capacities. For example, a guitar string company might sponsor a talented guitar player by giving him free strings in exchange for endorsing the company's product. They might also pay him if he is famous. Or, larger companies, like beer or soft drink companies, might sponsor a rock band's tour by funding the tour's travel expenses. They typically get their company name listed as a tour presenter on ticket stubs and sell their products exclusively inside the venues on the tour. Getting sponsored is typically not easy, though it can be beneficial for all kinds of musicians.
Research products and companies you would like sponsorship from. You typically get free products from companies that sponsor you, so start by finding companies that make products you enjoy using as a musician.
Get to know the product you seek sponsorship from. For example, if you wish to get sponsored by a specific guitar company, buy one of their guitars and use it frequently. If you call the guitar company and ask for sponsorship, chances are, the person you speak with will ask you what kind of guitar you play. If you say you play a different brand of guitar, they are less likely to sponsor you.
Focus on your playing. Play as many gigs as you can to improve as a player and build a reputation as a good musician and performer. Companies will not sponsor you unless you have a reputation that other musicians will look up to and want to buy products you are affiliated with.
Create a press kit to give to potential sponsoring companies. A press kit is kind of like your resume as a musician. It should include a brief bio about your career, head shots, shots of you playing and using their equipment, a discography of your recordings, a professional recording of your playing, current performing schedule and your contact information.
Call the companies who make products you enjoy and speak to Artist Relations departments. Ask how to get sponsored by them as a musician, and send them your press kit. Different companies have different policies and procedures. Also, different musicians have more credibility. If you are a famous musician, you can have your manager or agent make this call for you, and your chances of getting sponsored are good, since your brand and popularity will help promote the sponsoring company. If you are not a well-known musician, then you should be talented with a potential to become popular to be considered. There needs to be an incentive for the sponsoring company.
When you get sponsored, it is really you who is endorsing the company; the company is not endorsing you. They provide incentives to you, such as free products or money, to endorse and promote their company. Before you seek sponsorship, understand that when you are sponsored, you are a spokesperson for that company. If you do not like that idea, do not seek sponsorship.