Sorry to hear of your loss.
Distributions from a traditional IRA are included as ordinary income and are taxed the marginal rate of the taxpayer.
So, the amount of tax you will have to pay when the IRA is distributed will depend on you and your sister's marginal tax rate. Your marginal tax rate depends on your taxable income and filing status and ranges form 15 to 33%.
When you are required to take distributions depends on whether your father had begun to take distributions.
From http://www.irs.gov/publications/p590/ch01.html#d0e6046 :
Owner Died On or After Required Beginning Date
If the owner died on or after his or her required beginning date, and you are the designated beneficiary, you generally must base required minimum distributions for years after the year of the owner's death on the longer of:
Your single life expectancy as shown on Table I, or
The owner's life expectancy as determined under Death on or after required beginning date, under Beneficiary not an individual, later.
Owner Died Before Required Beginning Date
If the owner died before his or her required beginning date, base required minimum distributions for years after the year of the owner's death generally on your single life expectancy.
You can choose to take distributions greater than the required minimum distribution; but larger amounts could result in a larger marginal tax by adding more to your taxable income.
For multiple beneficiaries you should be aware that "As a general rule, the required minimum distribution rules separately apply to each account. However, the distribution period for an account is separately determined (disregarding beneficiaries of the other account(s)) only if the account was set up by the end of the year following the year of the owner's death."
More information is available in Publication 590, Individual Retirement Arrangements (IRAs) at http://www.irs.gov/publications/p590/index.html
I hope this general information is helpful even though the specific amount of tax due will depend on how you decide to structure the distributions and on your individual tax situation(s).
A discussion with a tax professional familiar with the IRA beneficiary distributions rules could be quite worthwhile to assist you to apply those rules to your specific situation.
My dad has had this IRA for many years and I NEED to "cash out" all of my part.
Again, how much tax will I have to pay to the IRS?
The tax on your distribution depends on the size of your share and how much other income you have before the IRA and your filing status.
At the end of the tables at http://www.irs.gov/pub/irs-pdf/i1040tt.pdf you can see the 2008 tax rate schedules.
For example, if you file single and had 35,000 taxable income a distribution of 40,000 would be taxed at 25% or 10,000 tax. Or, if you file single and have 100,000 taxable income a distribution of 40,000 will be taxed at 28% or 11,200 tax.
Online calculators are also available that you can enter your specific information to estimate the tax (such as at http://www.taxhelpinfo.us/calc-section.php?category=Taxes+%26+Payroll ).
Again, the amount of tax you will have to pay when the IRA is distributed will depend on your marginal tax rate. Your marginal tax rate depends on your taxable income and filing status and ranges form 15 to 33%.
If you want to give specific information I can look up your specific rate.
I hope this helps to clarify for you.