What are the Tax Implications from Alimony or Child Support?

Basically, child support has no effect on your tax return.
Alimony, however, does have an effect on your return. If you receive alimony, you need to make sure that you make Estimated Tax Payments throughout the year so that you do not owe tax when you file.

If you receive or pay alimony....
Alimony payments you receive are considered income and are taxable in the year that you receive them. The spouse that pays the alimony gets to deduct the payments.
Alimony income is reported by the recipient on Form 1040, Line 11.
Alimony paid can be deducted on line 31 of your Form 1040. You will need to have the recipient's social security number.

To be officially considered alimony by the IRS, a payment to one spouse by a former spouse must meet certain requirements. The rules state that to be considered as alimony, it must be paid under a divorce or separation agreement and does not include voluntary payments.
For divorce or separation decrees filed after 1984, the following must be true in order for the amount to be considered as alimony:

The payment is in cash
This includes check or money orders. It does not include transfers of services or property, execution of a debt instrument by the payer, or use of the payer's property.
The agreement does not state that the payment is not considered alimony
You can elect to designate in your separation or divorce agreement that the payments are not to be considered as alimony. You will need to attach the statement to your return each year.
The spouses are not living together at the time the payments are made
There is no liability to make any payment after the death of the recipient spouse.
If your agreement states that you must continue to pay the amount after the death of the recipient spouse, neither the payments made before or after the spouse's death are considered alimony.
The payment is not treated as child support

Alimony Recapture Rule
If alimony payments in the third year decrease by more than $15,000 from the second year, the alimony amount in the second and third years decrease significantly from the amount paid in the first year, or if alimony stops during that time, you are subject to the recapture rule. Reasons for a recapture could be:

Change in your divorce or separation agreement
Failure to make timely payments
Reduction in your ability to provide support
Reduction in your spouse's support needs

If the rules for alimony recapture apply, you will need to fill out the Recapture of Alimony Worksheet in Publication 504.

I receive/pay child support....

If you receive child support, it is not considered to be part of your income and is not taxable
Additionally, child support payments are not deductible by the payer

If you owe back child support...
You should know that past due child support is part of the Treasury Offset Program. This means that your refund or overpayment of tax may be reduced or taken to pay your past due child support. The Financial Management Service of the Treasury Department will take as much of your refund as needed to pay off the balance and any portion remaining (if any) will be issued to you.