To buy fine art, first educate yourself by visiting local galleries and finding artists with good reviews. Find artwork by the artists you researched, and choose a few that you like. Ask for the prices of the pieces you like, and then research the work's authenticity and whether the price is accurate. Be sure to purchase work that you truly like, and only purchase a piece that fits your budget. If you purchase well, the artwork's value increases over time.
Be sure to see the art in person before committing to buy it. If possible, interview the artists whose work interests you, asking questions about shows and gallery showings. Invest in fine art made by an artist whose popularity is growing, or who is beginning to have bigger opportunities to show work. Consider a piece that is in high demand, but is priced reasonably. Some galleries charge more for a piece based on the gallery's reputation.
Inspect the work before you purchase, or have a reputable dealer verify its authenticity. Once verified, purchase the piece. The right piece becomes more valuable over time. However, avoid purchasing a piece just because it is estimated to increase in value over time.
Purchase because you like it and you completed proper research on it. Even if the piece does not increase in value over time, its intrinsic value remains the same.