How many cards for a game key?

No idea, but I'm happy to trade all my cards for a key, if you're interested
i do know that 4 cards of any kind can get 1 ref, and that it's approximately 18-20 ref for a key
keep in mind that a high value catd can be exchanged for several garbage cards

Look through the trades section for traders who accept cards and ask them.

You usually don't trade cards for a really good game that's for sure. People usually trade cards for keys that have been free before but just didn't get one. People will usually specify how many cards they would want for a key if you ask. But it also cant be a bunch of super cheap cards unless your willing to hand in a lot more than the asking amount (and the opposite for more expensive cards)

Depends. If you got 3-5 games keys in a 1 dollar bundle for example, around 10 cards is fair enough.
Don't agree with the first person that a key is worth around 80 cards...

Depending on the game value in the trading community, keep in mind:
6 complete card packs = 1key

Do the maths

I usually ask and pay about 4% of the original undiscounted store value of a bundle game in cards, using the current minimum store offer price of a card as baseline. So a 10-dollar bundle game for 40 cents in cards.

I think it was 35 cards for 1 key, but now it's around 45 per if I'm correct.

use this to determine each card value and a cs go vanilla key is more or less 2 euros or 1.9 euros for tf2 key

That depends on the game you want to trade and what you want for it. I used to trade cards for games that were given away for free and only wanted half the value of the cards the games drop, so basically 3-5 cards. I used to trade away some CS:GO skins I had and wanted the value in cards (minus market fees). I used these cards to trade them for a game in return - non-bundled, mind you - and traded 7,- € worth of cards for it if I recall correctly. The lowest price for the game was 5,- € at the time, which I missed out on, though.

a card is generally worth their Community Market value which trends around 0.05 to 0.1 cents depending on card type.
Now compare to the estimated value of the game you are trying to obtain and voila.