A Canasta hand is scored in two parts. First the bonuses: five hundred for each natural canasta, three hundred for each mixed one, a hundred for each red three (eight hundred for all four, and against you if your side never melded), and a hundred for going out, or two hundred for going out concealed. Then the cards: the value of every card your side melded, minus what is left in both partners' hands.
Add the two for the hand and carry the total. Your side's first meld of a hand has to reach a minimum that depends on your score when the hand began, so the sheet has a column to note it. The first side to end a hand on five thousand or more, ahead of the other, wins.
At other tables
In classic Canasta the first meld must be worth fifteen while your side's score is below zero, fifty up to 1,495, ninety from 1,500 and a hundred and twenty from 3,000. Source: pagat.com
This is how Cards Royale scores Canasta. The full rules are on the how to play Canasta page.