Adding taxes increases the price of a good. Increasing price causes a decrease of demand. In order to return to a profit-maximizing price, firms must then decrease the prices of goods (and reduce output*.) The firm's share of the tax is the amount they need to lower the price. The household's share of the tax is the cost of the tax, minus the price decrease.
Households never pay the entire amount of any sales tax, because demand always responds to price. Arguably, households don't even pay the entire amount of income taxes either, because the supply of labour responds in a similar way.
(* An astute reader will note that, due to the reduction of supply and demand, the total cost of the tax to the economy is greater than the amount which is actually paid to the government.)