If my adjusted gross income is $1000, and I make a donation of $100, then it seems that I'm still going to have to pay a tax on the $1000. The donation is deductible, so I don't pay any tax on that, but it hasn't reduced my tax bill. From saving on taxes perspective, what is my incentive to donate?
If you itemize your deductions (I'm assuming USA here) then qualifying charitable donations (say, $100 to your church) can be deducted, which means they're effectively an offset to your taxable income.
Your adjusted gross income already takes into account any deductions, including charitable contributions. So, after all is said and done, if your AGI is $1,000, your tax is calculated on $1,000. If you didn't make that $100 contribution, your tax would be calculated on $1,100. That's where the tax savings you smell is located.
Let's imagine you're in the US, there's a flat tax of 20% on all your income, and you're itemizing your deductions.
If you made $100,000 and didn't do anything deductible, your adjusted gross income would remain $100,000, and then you'd pay $20,000 in taxes, so you'd be left with $80,000 after taxes.
If you made $100,000 and donated $10,000 to a qualifying charity, your adjusted gross income would be $90,000, and then you'd pay $18,000 in taxes. So after the donation and taxes, you'd be left with $72,000.
The net result is the charity got $10,000, but your take-home only dropped $8,000, with the government picking up the $2,000 difference. You're still worse off, in terms of your personal cash, than if you hadn't made the deduction. It's just that the bite isn't as bad as it might have been.
It's a little more complicated in the real world where you have marginal tax rates that vary with your income level, but the principle is still the same. If you donate $X, your tax bill will drop by something less than $X.
So I make charitable donations for my own reasons. The tax deduction is icing on the cake, and it can affect how much I donate because the government is picking up part of the tab, but it doesn't affect whether I donate or to whom.
I've heard claims of wealthy people making donations of $X to drop their tax bill by more than $X, but every one I've heard of was something really complicated, used obscure tax loopholes, and involved a donation of art, a building, or securities rather than just money or a check. If you're in that world, you really should retain a tax accountant.
The donation is deductible, so I don't pay any tax on that, but it hasn't reduced my tax bill
Why would you expect to pay taxes on a donation? It's not income. That fact that it is tax deductible does not mean that you do not owe taxes on it. You do not owe taxes on it because it is not income.
The tax deductible donation impacts your adjusted gross income, but only if you itemize deductions. If you take the standard deduction, a tax deductible donation has no impact on your tax liability.
From the horse's mouth, with emphasis added:
Whether to itemize deductions on your tax return depends on how much you spent on certain expenses last year. Money paid for medical care, mortgage interest, taxes, charitable contributions, casualty losses and miscellaneous deductions can reduce your taxes. If the total amount spent on those categories is more than your standard deduction, you can usually benefit by itemizing.
Charitable contributions that exceed the standard deduction are deductible. I believe the 2010 Standard Deduction is $5,700 for an individual and $11,400 for a married couple.
Typically, you don't get a deduction unless you own a home, since the mortgage interest and local taxes are generally deductible. YMMV.
How much you save by deducting income is specific to each individual. For me, my combined Federal and State tax savings are about 30%. So if I donate $100, I effectively reduce my tax obligation by around $30.