If my paycheck says federal withholding, does that mean I have already paid taxes to federal and I can say as such?

[Critter-3]

You did not "pay" taxes you had taxes withheld.  When you get your W-2 it will show the gross income and the federal/state taxes that were withheld and both go on your tax return.   If you paid in too much thru withholding you get a refund when you file the return.  If you did not have enough withheld then you will owe a balance due. 

[xmasbaby0]

Ia this your first job---first time to prepare a tax return?   At the end of January your employer is going to issue a W-2 to you that shows how much you earned and how much tax was withheld from your paychecks.   Your W-2 will show how much was withheld for federal tax and how much was withheld for the state's tax (if you live in a state that has a state income tax).   You will enter all of the information from each box of the W-2, and the software will calculate whether too much tax was withheld---if too much was withheld, you will get a refund.  If not enough tax was withheld, you will owe and need to pay.

https://turbotax.intuit.com/tax-tips/irs-tax-forms/what-is-a-w-2-form/L6VJbqWl5

[rjs]

The federal withholding on your paycheck is a down payment towards your total tax for the year. When you file your tax return it will calculate the total tax that you have to pay for the year, and it will apply the "down payments" (the withholding) to the total.