Different expert here.
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The first thing to do is get an Employer ID number (EIN) from the IRS. While you get them from the IRS, the KS stat website discusses these and provides a link to the IRS page at http://www.kansas.gov/business/fein.html
The Kansas Dept of Labor also has an excellent website, much better than most states, that allows you to do everything through them, including paying the employment "taxes". That web page is https://www.kansasemployer.gov/uitax/account/Register.aspx
Using that website you can complete the Status Determination Report, K-CNS 010, apply for a state unemployment tax number, and report changes to your existing account, file your Quarterly Wage Report & Unemployment Tax Return, K-CNS 100. They will also provide publications to you explaining how to do all of these. They will also walk you through the process if you have any problems.
Other than these things I have set forth above, the only other issues are, first, what type of business do you want to have to pay the employee(s). I'm not sure how you are set up now but you can incorporate or form a partnership or you can operate as a sole proprietor. If you want to operate as a corporation or partnership then you need to draft and file the appropriate paperwork. You can do that by buying the forms and having them filled out at a website like this one or by hiring a local lawyer to handle the paperwork and then advise you on how to "act like a corporation". There are a number of reasons to use a corporation such as to avoid personal liability and also to cut down on taxes.
You also have to consider whether or not you want to carry workmen's compensation insurance. It is required of KS employers except for those in certain agricultural pursuits or those with a gross annual payroll of $20,000 or less. There is a web page that discusses this topic at https://www.dol.ks.gov/WorkComp/FAQemployer.aspx