Commissioning is simply a custom piece created for the client (you). So, when you have a piece created by an artist to your specifications (size, colors, theme, etc.) you've acquired a commissioned artwork. Sound fancy!!
However, if you want to have a pleasant experience when commissioning a painting; here's a huge mistake to avoid. Always look at the artists' work first! I know, I know you're probably thinking this is too obvious, but I promise you it isn't. See what happens many times is that a patron (client) will want a painting created, he/she is excited and has something incredible in their mind as to what the artwork should look like. And the main mistake is that they'll usually go to the nearest artist (someone they like and trust), and blindly trusting on the fact that their friend is an artist...they'll ask for the painting done without making sure if the artist is suitable to create this special artwork.
There's nothing wrong with going with an artist you like and trust, but make sure to find out if they create the type of artwork, skill level, and discipline to create the artwork you want. For example, you may want a portrait of your little girl done in a very lovely classical or Impressionist manner (like John Singer Sargent's work), but the artist you contacted is an abstract cubist painter (like Picasso). And you may end very unhappy. Because the artist told you that he/she could painted what you were asking, but never showed you how you would be painted.
Either way, you get the point. Always check the type of work of the artist first, so that you have no unhappy surprises. I'll leave you with that for today.