Best way to go about it is to find artists whose style or subject matter appeals to you the most, look over their prices, and evaluate for yourself if the prices for commissions offered is a good fit for what you're looking for and is something that you can justify paying for or is in your price range. Then, when you've settled on one, contact them through a private message on the site (you can click on their profile, and at the bottom of the page there'll be an option to "send message") that you're interested in commissioning them. You can also contact them through deviantArt, tumblr, or other sites where they put up their artwork and post commission prices. There are some threads in the forum section where artists have provided those exact details, but you can also search for them on those sites or ask around if need be.
Be sure to provide as many details as you can on what you want in the commission, taking into account the prices they'll have listed for having multiple characters, backgrounds, objects, coloring, different poses or kinds of fabrics, and so on. Be detailed and be patient, as sometimes it may take an artist a while to get a response back due to handling other commissions they're working on, as well as taking care of obligations in their own life.
Some artists will want to have payment up front, some will take payments in installments as they do the work for you, some will take half at one point and the other half on completion, and some will only take payment after they've reached a point with your commission that they feel will best represent the final product and you've okayed it. Just remember that you're engaging in a kind of business contract with the artist. Be respectful to them, but do check in with them to see how things are progressing if it's taking time; I feel that it's best to check in with an artist every three to four days if they don't maintain a more frequent period of time with contacting you. Be friendly, show that you know what you want in the commission you're asking, and unless they offer to do a package deal or a discount for you, don't bring those up (unless you're a regular commissioner of them, then you can politely ask about the possibility, and if they decline, don't take it too harshly or think that's the end of that, because they might consider it or bring it up at a later date). You should always go into commissioning an artist with the attitude that you may commission them again in the future, and that artists will talk about who's been a good client and who hasn't with each other.
Other than that...I think that's all I can think of that should be mentioned. Just going over how I've approached commissioning others in the past. I hope this helps, and I think the mods will be okay with this thread, seeing as the title of the thread is appropriate to what you're asking about. I know that some people might not find the answers they're looking for in the stickied threads in the forums, so most times the mods won't be hard on you for posting threads with inquiries. The most they'll do is provide a link to a relevant thread and direct you there before closing your posted thread down, more to keep things tidy than anything.
Anyway, good luck to you in finding an artist, and if you already have some in mind and have them picked out, I hope you enjoy what they make for you. ^^
