For the ETF you do not transact with other buyers and sellers.
Vanguard and other providers like State Street and Blackrock, employ investment banks to act as "market makers".
There will always be liquidity, however the market maker takes a small cut, being the spread between the bid and offer price.
When you buy, the market maker delivers your cash to the fund, and the ETF provider creates the units in the underlying fund for you. When you sell, the reverse happens.
That's the gist of it anyway...