My wife is self-employed and we file married jointly. Does she need to pay estimated taxes and if so how do we calculate them?

If your wife has over $400 in profit, she will need to pay taxes on her self-employment income.   Here is the IRS Estimated Tax page.

If you want to do the estimate yourself, here is a step-by-step WikiHow article with all the steps. 

A penalty is accessed for underpayment.  Generally, most taxpayers will avoid this penalty if they either owe less than $1,000 in tax after subtracting their withholding and refundable credits, or if they paid withholding and estimated tax of at least 90% of the tax for the current year or 100% of the tax shown on the return for the prior year, whichever is smaller. 

Whenever I am self-employed, I use Intuit Quickbooks for my business recordkeeping.  One of the things that Quickbooks does for me is calculate my estimated tax payments.  Each quarter, it lets me know if the payment I am making is enough to cover my estimated payment for that tax year.