Well, you've got to estimate your taxes, then send them in. Quarterly - April 15th, June 15th, Sept 15th, January 15th are the due-dates.
Easy part is sending them in -
https://www.eftps.gov/eftps/ lets you do this electronically - easy and free.
Estimating - at minimum you have self-employment tax. Basic computation is: Contractor Net Income (after business expenses, if there are any - before retirement contributions like individual 401K though) * 92.35% * 15.3 % (assuming your wife is not going over the social-security wage limit of $118K).
Then you've got federal income tax to consider. The case-study spreadsheet in the sticky "How to write a case study" at the top of "Ask a Mustachian" can help with this. Since this involves all sources of household income, not just the contractor income, can't help with specifics.
And since you're in South Carolina, you have state income taxes to deal with too. I live / work in Florida, where we don't have state income taxes, so I'm no help there.