The U.S. Customs and Border Protection collects tariffs. There is a complicated process for them to determine the category a product fits in, and then they invoice the importer for any tariffs duties, or fees.
Filing a formal entry (for goods valued at $2500 or more)
No more than a week before the expected arrival of your goods in port,
or no later than 10 days after arrival, fill out CBP forms 5106
(Request for Importer Number, or Notification of Importer Number),
7501 (Entry Summary) and Release Document. Purchase a Customs bond (or
be prepared to post cash in lieu of bond). Bring the paperwork and
bond to the CBP port, entry branch, and ask an entry specialist to
review your completed forms.
Obviously companies who do this everyday follow a slightly different process but the tariff is collected at the port of entry by CBP.
Additional information based on a comment:
"US businesses don't pay tariffs to the US. You asked if "US businesses are handing over actual cash to (the IRS, else who? to) pay the tariffs". Chinese companies pay tariffs on their exports to the US, to the US."
- If a computer manufacturer imports the parts they pay the tariff.
- If a retail company imports the items for sale they pay the tariff.
- If a wholesaler imports the item they pay the tariff.
- If a company in China sends the items to the US and then sells them to other companies or the public then the Chinese company pays the tariff at the border.
In the last case the money is paid by a Chinese company, but in the other cases it is paid by a US based company. It generally depends on how the shipping costs are figured. In some contracts "FOB shipping point" the sale takes place when it leaves the selling company, and the new owner handles everything after that point. In other cases "FOB destination" the sale is only when it is delivered to the buyer, the seller has to handle the costs.
It will depend on the person making the transaction on the port of entry. CBP will collect their money/bond to release the goods.
The questions were "how/when/where" and to which organization "the IRS, else who? to". The answer is to CBP at the port of entry, with cash or a bond.