Take classes in your artistic discipline. Research the institution. Pay special attention to which venues regularly work with the institution to show student work. Colleges and universities often have connections that no amount of money can buy. These relationships are usually free for students to exploit.
Join an art club. These groups are everywhere, and your city is likely to have at least one. Art clubs provide an organized group of artists who can pool their energy into finding locations for the artists to show their work. Often these groups are well-established and have relationships in the community with merchants and restaurateurs who agree to regularly display work from the club's artists.
Enter any available art shows or art festivals in your area. These are generally annual or semiannual events where anyone can show their art for the price of the entrance fee. These events are often held in heavily trafficked places like public parks and shopping malls. Events like this expose a large cross section of your community's population to your art.
Donate your work to charities for inclusion in their auction fund-raisers, or to organizations such as hospitals that have locations to display your work.
Pay attention to the artwork displayed in every place you pass through and look for opportunities to show your own artwork. Opportunities are often present in places you wouldn't normally think of, such as airports, restaurants, corporate lobbies or galleries and government buildings.
Keep a portfolio of samples of your work and the places and events where your work has appeared. Use it to market yourself to private galleries.
Talk with gallery owners and curators. Use your portfolio to present samples of your work and show evidence of the public exposure you've gained. Pitch your work and your ideas for showing it. The more familiar, local gallery personnel are accepting your work, the more likely they are to invite you into the ranks of artists who show with them.