How to get Steam trading cards for free, and why it is slow

The only cost-free source: cards drop automatically while a game is running, up to half that game's set. No purchase, no gems, no trading required, but capped at half a set and paced at roughly one card per thirty minutes of play.

Duplicate cards, and cards from games that are not being worked toward, can be traded to someone else for the specific cards that are needed. This costs nothing but requires finding someone with a matching want, which is slower than it sounds for anything but the most popular games.

Cards and other items can be turned into gems, and gems can be spent on booster packs. It recycles what is already owned rather than creating anything new, and a booster pack's three cards are random, so this is a slow, indirect way to fill a specific set.

Every free method is genuinely free, and every one of them is slow measured against a specific target level. That gap is exactly what buying ready sets is for; it is a different trade-off, not a different rule.