An artist's primary goal is to produce a successful painting. That is and will always be front and center. But the devil is in the details and making a professional package is a significant part of the impression you make with your art.
I was slow to come to the table about how my paintings looked on the backside. My hanging hardware wasn't always the best. I often forgot to label the back of the painting appropriately. These things are important too, especially if you are putting your work out there for sale. It is also important for posterity if you give your work to family or friends.
I am a member of an art guild. We hang regularly in a very nice public place and I am one of those responsible for the hanging. I have been very surprised at how many experienced painters neglect the back side. Not only does this detract, it makes a world of headaches for those who hang the art. Galleries and juried shows have very strict rules about this so it is good to learn them early on.
Here is what I now do and recommend-
This is called D ring picture hanger. It is also sometimes called a mirror hanger. These can be bought for a very small amount on many websites.
This is how it looks installed. All you need is a small hand-held electric drill or a screwdriver.
They should be the same distance below the top of the frame. Like this- about a third of the way down is recommended. I prefer the wire to be slightly loose but not too loose. If very tight it can be difficult to get on the hook.
Whatever you do, do not use the following hardware pieces-
Screw eye- not very stable, too easy to twist and turn, looks bad.
Don't even think about it- the very worst option. Yes you can wire around it but it is un-hangable on many hanging systems and looks very unprofessional.
Last, make a label for the back with the following information.
Title of Painting
The year it was painted
If your painting is a gift or commission for a special occasion you might consider making a personal note as well. Or suggest that the gift givers do this if applicable.
Attach your business card on the back in case the buyers want to follow your work or reach you in the future.
Happy Painting, and don't forget to make your work look great on both sides!