I have just excepted a job where I will be getting a 1099 instead of W2. My question is how do I figure the amount of money to put aside for taxes each week?

You are independent contractor. You will report your income and expenses on schedule C or C-EZ (Form 1040). This income is subject to SE tax at 15.3%. Read: Your U.S. Tax Return: Tax Filing by Self Employed Sole Proprietor or Independent Contractor

Since NO taxes are withheld, you should put aside 30% to cover income and self-employment taxes.

You also need to start making quarterly estimated tax payments using Form 1040-ES.