You will have to pay federal income tax on your royalties and possibly state income tax depending on where your minerals are and how much income you have.
For income tax, you will have to determine if the extra income from royalties is going to boost your income to a level where the IRS might enforce a penalty. If you are already paying quarterly taxes, simply add the income to your estimated tax calculations at the end of each quarter. Here’s the quote straight from the IRS:
“Generally, most taxpayers will avoid this penalty if they owe less than $1,000 in tax after subtracting their withholdings and credits, or if they paid 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.” You can read the entire note here: Topic no. 306, Penalty for underpayment of estimated tax | Internal Revenue Service
Property taxes are a different animal. The appraisal district will make an estimate of what your minerals are worth and you’ll pay the normal rates based off of that. I’ve seen estimates that were ridiculously high and low, so you never really know what you’re going to get from each county. There’s an article under the “Help” tab above, but it can be found HERE: http://www.mineralweb.com/owners-guide/leased-and-producing/royalty-taxes/ad-valorem-taxes/