I would like to know if the custodial parent is single and doesn't work and I pay child support am I allowed to claim them on my taxes

No - the custodial parent claims the child as his/her dependent unless either (a) your divorce decree specifies that you can claim the child as your dependent, or (b) the custodial parent grants you permission to claim the child by providing a signed Form 8332 for you to include in your tax return. However, if you are sure the custodial parent is not filing a tax return you may be able to get away with claiming the chld yourself. But I would suggest you and your ex reach agreement about this, or you could find yourself being dinged by the IRS if two people file retuns both claiming the child.