First the active player identifies the creature they control with the highest mana cost (and chooses one if there's a tie) and chooses whether to sacrifice it or pay mana. Then each other player in turn order does the same. All creatures sacrificed this way are sacrificed at the same time.

Although Tariff checks the mana value of the creatures on the battlefield, you need to pay the creature's actual mana cost (including color) to keep it on the battlefield.

The choice of creatures is made on resolution and not on announcement.

You can use mana abilities during the resolution of this spell if the player decides to pay the mana cost.

You choose whether to pay or not on resolution. If not, then you sacrifice the creature. You can choose to not pay if you control no creatures on resolution.

Tariff : règles, fonctionnement et interactions (MTG)

Tariff is one of those cards players keep asking about. Here is, in plain words, what its official text says, the rulings published by Wizards of the Coast, and the combos players actually run.

Official card text

Each player sacrifices the creature they control with the greatest mana value unless they pay that creature's mana cost. If two or more creatures a player controls are tied for greatest, that player chooses one.

How it works : Tariff

Original English text — Wizards of the Coast / Scryfall

#1April 1, 2008· Wizards of the Coast
First the active player identifies the creature they control with the highest mana cost (and chooses one if there's a tie) and chooses whether to sacrifice it or pay mana. Then each other player in turn order does the same. All creatures sacrificed this way are sacrificed at the same time.
No other card is named in this ruling.
#2April 1, 2008· Wizards of the Coast
Although Tariff checks the mana value of the creatures on the battlefield, you need to pay the creature's actual mana cost (including color) to keep it on the battlefield.
No other card is named in this ruling.
#3October 4, 2004· Wizards of the Coast
The choice of creatures is made on resolution and not on announcement.
No other card is named in this ruling.
#4October 4, 2004· Wizards of the Coast
You can use mana abilities during the resolution of this spell if the player decides to pay the mana cost.
No other card is named in this ruling.
#5October 4, 2004· Wizards of the Coast
You choose whether to pay or not on resolution. If not, then you sacrifice the creature. You can choose to not pay if you control no creatures on resolution.
No other card is named in this ruling.