According to Valve, they have announced that Artifact will be released on the 28th of November, 2018 where it will be available on the PC, Mac, and Linux. There will also be a mobile release except that iOS and Android players will need to wait until 2019, but in the meantime players will be able to check it out on their computers.
As for pricing, Valve has priced Artifact at $20 where it will be launched with 280 cards, and just like a physical trading card game like Magic: the Gathering, Artifact cards can be sold and bought via the Steam Community Marketplace. As Touch Arcade points out, this seems to be a feature lacking in other digital card games such as Hearthstone which should make it rather interesting for those who are bit more entrepreneurial.
For those who can’t wait that long, Valve has also confirmed that Artifact will be playable at PAX West which takes place at the end of the month, so if you are going to the event then you can check it out.