If I paid my children (under 12) in cash for work related to my S-Corp, how do I enter it as an expense for my self employed income?

[Hal_Al]

Your S Corp must issue them a W-2.

See https://www.kitces.com/blog/tax-rules-hiring-children-family-business-flsa-tax-savings-standard-dedu...

[Critter-3]

You should also have issued a W-2 for yourself ... if you have not then seek local professional assistance to get you up to speed on the filing requirements of an S-Corp.  

The IRS position is that an S-Corporation MUST pay a reasonable compensation to an officer before non-wage distributions may be made.  The reason is that they feel that non-wage distributions when no wages are paid is an avoidance of social security taxes.  From the IRS website at http://www.irs.gov/businesses/small/article/0,,id=203100,00.html :

"Reasonable Compensation

S corporations must pay reasonable compensation to a shareholder-employee in return for services that the employee provides to the corporation before non-wage distributions may be made to the shareholder-employee. The amount of reasonable compensation will never exceed the amount received by the shareholder either directly or indirectly.

Distributions and other payments by an S corporation to a corporate officer must be treated as wages to the extent the amounts are reasonable compensation for the service rendered to the corporation.

Several court cases support the authority of the IRS to reclassify other forms of payments to a shareholder-employee as a wage expense and subject to employment taxes."

The page cites Joly vs. Commissioner, 211 F.3d 1269 (6th Cir., 2000) as one judicial finding on the IRS's authority to reclassify distributions to wages subject to employment taxes.  Factors to determine reasonable compensation are given in the ruling.

The AICPA has an interesting article on this topic here: http://www.aicpa.org/publications/taxadviser/2011/august/pages/nitti_aug2011.aspx

You also might want to read a lively discussion on the Tax Almanac website here: http://www.taxalmanac.org/index.php/Discussion_Forum_-_Tax_Questions .  The substance of the discussion seems to be that taking a reasonable salary is not optional and, if you took distributions with no salary, the distributions should be changed to salary with appropriate employment tax returns being filed (late, if necessary.) 

The fastest way to get audited as an S-Corporation is to not report wages to officers on page 1 of the return.

[tagteam]

@Critter-3 The AICPA link did not work but the one below does (FYI).

https://www.thetaxadviser.com/issues/2011/aug/nitti-aug2011.html

[SweetieJean]

@Critter-3 has given you some good advice.  You really need to see  a local professional.

It appears that you want to claim the S Corp's expenses on Schedule C of your own tax return. That is not correct.  Rather, the S Corp must file its own return (1120-S), and then issue a K-1 to the Shareholders (you), which they then report on their personal returns.  See, for example:

S Corporations | Internal Revenue Service (irs.gov)

S Corporation Compensation and Medical Insurance Issues | Internal Revenue Service (irs.gov)

Also be aware of Federal, State and local labor laws, especially since you indicated that your children are under age 12.