How does game trade work?

I have spare copies of some games bought in various past 4-pack offers.

How can I trade one of them with another user? If I click an item I don't see any Trade button, but only gift.

Solution 1:

In your friends list, right click a user and press "Invite to trade." In there, you'll be able to send unused copies of games and items from several supported games. Trading supports game copies for game items and items between different games, with no real limits.

At the moment, the supported games for item trading are:

• Team Fortress 2 items (hats, scrap metal, weapons, crates, keys, etc.)
• Portal 2 (cosmetics)
• Spiral Knights (materials, weapons/cosmetics/armor that are unbounded, CE; crystal energy and crowns)
• DotA 2 (consumables, couriers, announcers, gear, backgrounds, etc.)
• Steam (gifts, backgrounds, cards, emoticons, gems, etc.)

Solution 2:

From the Steam FAQ article:

Any game you’ve purchased from the store as a gift, or received as an Extra Copy, can be traded to other users. They can be used to trade for other Gifts, or for items in Team Fortress 2 or Spiral Knights. We’ve added a new checkout option to the Store when purchasing a gift so you can save it for trading or sending later, to support users who want to save games for trade fodder.

Additionally

Only gifts that are purchased on trusted accounts can be traded immediately; otherwise there is a 90-day cool down before the gift can be traded. Any account that has made any valid purchase from the Steam Store more than 90 days ago is considered trusted. This is to ensure that all games traded are valuable, and help prevent fraudulent purchases for the purpose of trades.

It might be the case that you fall into that "non-trusted account" group.