Okay, let’s get some things out of the way real quick regarding monetization:
Is Artifact free?
No, it costs $20 and there is no free alternative.
What do I get for buying it?
Two complete decks, ten booster packs, and five tickets (used for playing competitive modes). This is more than a $20 value considering the booster packs alone would cost that much, and tickets also cost money.
So even playing the game costs money in the form of tickets?
Competitively, yes. However, you can play an unlimited amount in casual play without spending any extra money.
How do I earn more cards?
By buying them in boosters, buying them on the Steam Marketplace, or winning in competitive modes and being rewarded with booster packs.
The bottom line is there is plenty here to keep you busy without spending any extra money unless you're very interested in building your own decks and playing with them. If you have other questions about the basics, it's probably answered in the cleverly-named ArtiFAQ.