Where can I find if I am paying state taxes? Can I see it on my W2?

Your state tax is shown on your W-2 in boxes 15, 16 and 17.   When you enter a W-2 into the federal return make sure you enter every box that has an amount.   

W-2 Box 17: State Income tax –represents the total of state income taxes withheld from your paycheck for the wages reported in Box 16.