Well, I think many start out mixing by themselves if they dont already know a mixer? and generally once they get into the community they meet mixers??? If you cant find one, maybe search for advice on what other mixers use, or ask them which programs are easiest for a beginner?
Sorry I can't be of more help on that, I don't know any mixers myself >w<! But if my advice isn't helpful perhaps you'll get another response.
Well, I know there are a lot of mixers for hire on NND, but you might have some better luck contacting some of the Youtaite mixers if your Japanese isn't up to snuff. DM-ing on Twitter or e-mailing them seem to be good ways to contact people, though I've never tried it myself. Though some of them might accept right away, it's always best to befriend people (for real, with no ulterior motives) before asking them for their services.
But if you're a bit impatient like me, you can do what Candii said above: start by mixing your own covers, and once you become part of the community and meet more people, you can ask around for mixing/encoding help.
I personally recommend practicing first in Audacity to get your feet wet if you have no experience with mixing, then graduating to Adobe Audition or other more advanced editing software. I'm horrible at mixing myself, so I'm afraid I can't give any advice other than that.
There's also a tag on niconico that links together a lot of mixing tutorials, how-to-do-harmonies for various popular songs and other useful things for new and aspiring utaite, so check that out too if you're good at Japanese.