If you're good at social media, you really shouldn't need to advertise, so absolutely! (Okay, I'm being a little cheeky, there.)
Of course, you say you don't have much experience. In a field where things change so rapidly anyway, 5 years experience isn't necessarily better than 6 months experience, if the newbie is clever and motivated.
Obviously, learn everything you can about social media marketing. Master Hootsuite. Be able to answer questions like, "How can businesses use Vine?"
If you want to be really clever about this, put up a blog and blog your way through your learning. As you learn about how to sell on Instagram, write a blog post about it (and give credit/links where they're due!)
Transparency won't hurt you here. If I read your blog and saw that you spent the last three months teaching yourself about social media and writing about what you learned, I'd be impressed. I wouldn't care that you didn't know anything three months ago, since I really don't have time to spend three months cramming on this topic; I'd be happy for you to do that for me.
You can start working for real clients by taking on nonprofits and doing social media for them for free. Or a friend's small business, if you want. But ONLY work for free if you get permission to TALK ABOUT IT, share details, use screenshots, etc. And only work for free over a limited time.
For free work: Create a simple written agreement that says what services you'll perform over 6 weeks, or 3 months, or whatnot, and that either party can terminate during that period, and that if the pro bono engagement lasts the entire term, the client will give you a written recommendation (associated with their name and business) that you can use on your website and on LinkedIn, and you can use any other details.
At the end of the free period, the client would then have the option to continue working with you for a monthly retainer if they choose to do so; if not, you'll leave them with a short manual on how do maintain their own social media.
Also keep in mind that, in order to sell expertise, you often only need to be about two levels above who you're selling to. Social media for a major corporation may involve detailed analytics and a video production team. Social media for a church down the block may involve starting a Twitter account, explaining what Twitter is, establishing a few hashtags and getting the word out to members, and suggesting the types of things a church might want to tweet.
Boom, now you have a social media agency.
