Possibly nothing. There are too many possibilities involved to say with absolute certainty that you will owe no tax.
There is no federal inheritance tax. Some states do tax inheritance, but generally do not when it is parent to child. I can't say this is true with every state.
However, the type of money involved can determine if there will be tax at the federal level. If the money was cash in the bank, no tax. If the money was in stocks or bonds, the cost basis to you of those assets is their value on the date the person giving it to you died. This is a tax break for you by not valuing those things at what they paid. When you sell those things, their value the day you sell may be more or less than on the day they became yours. You would owe tax on a gain and may be able to take a tax loss on a loss. The same thing applies to physical assets that you don't sell but hold onto, and valuables should be appraised so that you have hard evidence of their value at the time you acquired them.
But if you inherit money in an IRA or 401K account, the IRS wants their cut. This is not inheritance tax but deferred income tax, tax that was not paid on the contributions and earnings. If you take all of the money, that will be taxed as ordinary income to you. If this applies to you, I can give you a tip on how to minimize that tax.