Here is where you go to register your business. http://www.sos.state.ok.us/business/busi鈥?/a>
I would however suggest that you also talk to a business counselor before you do anything especially spend money. I'd call the local Oklahoma office of SCORE (go to http://www.score.org and input your zip code to find the chapter nearest you), the advice is FREE.
The counselor at SCORE will most likely advise you to write a business plan which is very good advice because it will force you to dig out all of the start up details and the costs of starting a day spa and force you to also understand all of the aspects of this business including the customers you'll concentrate on (your market ) and how you'll go after them.
Try this link :
and read some of the articles especially the ones about a business plan and starting a business.