1 - You can barter with an artist or gallery. Many North Americans like myself, feel bad about asking for a better price. We don't want to belittle the artist or devalue the work but, everyone has a budget. If the asking price isn't what you can afford, ask for a discount. Some artists might take offense, some artists will respectfully decline, but most artists will work with you. If you don't achieve the price you want, there's more options like the next 3 tips.
2 - You can make payments. Just like any store, you can work out a payment plan with the artist. A prepared artist will be able to create invoices for you and set you up with plan that takes payments on set dates. The artwork will almost always remain in the artists possession until the last or second last payment is made. Sometimes, you'll want the artwork in your hands undamaged before you release the last payment.
3 - You can rent-to-own. If an artist offers to rent out a painting and you like it, you can complete the payments as per the above two methods minus the rental fees. Why would anyone rent artwork? Staging a home for a sale is a common reason to rent artwork. Sometimes you want to know if you will get sick of the artwork, so you can rent it for six months and see if you still like it after that. If an artist doesn't advertise renting, just ask. Most artists are flexible but it may take some convincing as they need to draft up a contract for legal reasons in case of damage or theft.
See more about renting art here.
4 - You can try it out. This one is cool. Within a reasonable distance from the artist, you can ask the artist to loan you the artwork for a weekend. This is usually no charge but again requires contracts for potential damage or theft. Damage and theft rarely happens but no one wants to take that chance. So why would you want to try it out? Because it's important to know if the work will fit the space you want, or go with your furniture, or be the conversation piece you hoped it would, and simply just love it as much in your home as you did online or wherever you saw it. But Again, this is rare and in most cases requires you to be within driving distance of the artist.
5 - You can honestly say you own an original. Who cares about an original? Believe it or not, lots of people care about originals. People connect with artwork and are inspired by what they have in their homes. An original isn't something that just goes to a second hand store the moment you change your furniture. And imagine you stepped into someone else's house and saw the exact same print you got at Liquidation World or Walmart?! Oops, guess you have the same taste as the next person. Individualize your space. Make it yours. Make it Unique. Buy original.