The amount of tax would depend on your filing status, other income, deductions, and the amount of taxable income incurred on the surrender of the annuity. If it is a nonqualified annuity then the taxable portion is the difference between the proceeds received (assuming the entire contract is surrendered) and the total investment in the contract. If it is a qualified annuity (a retirement account such as an IRA or 403(b)) then the entire amount is taxable unless you had after-tax contributions in prior years (these would be recovered tax-free).
There is a 10% penalty on the taxable income portion if withdrawn prior to age 59 1/2.
The amount of state income tax would depend on the your state of residence.