You may Trade with your neighbors Resources and Rare Goods, 1 for 1. To do so, click their city from the Neighbor Strip in the bottom of the screen. Once their city has loaded, click the Trade icon in the bottom right.

Trade menu icon

This will bring up the Trade Menu.

To propose a trade, click 1 item from their strip (at the top) to trade with one resource of yours (at the bottom). Once you have the Trade you would like to propose, click the "Trade" button.

This will send them both a Wall Notice and an in game message proposing your trade.

Trade menu

They have to go to their messages, find your trade proposal, and then can decide if they want to accept the trade proposal or ignore/delete it.

Messages menu

Trade proposals in the messages are blue.

Trade example

Being only able to trade one item for another is check against cheaters who build multiple "farm" accounts whose goods they then funnel to their own main account. On the Trade Forum sometimes trades are proposed "2 iron for 1 Gold". That usually means Trading 1 iron for 1 gold, then trusting the person to also accept a second trade of 1 iron for something useless like Tar or any of the other misnamed Rare Goods. Not everyone can be trusted, but the fact you have to friend them first and will know their facebook account at least lets you complain about being ripped off on their Wall afterward if they cheat you.

There is much debate about what is a fair trade.

In general, Rare Goods are worthless. Never trade away any of your own Resources for any Rare Good. You should also try (as much as possible) to trade the same level Resource with another. This isn't always possible (a lot of things need Iron for some reason), but trading Redwood for Red Marble is a more fair trade than trading Redwood for Sandstone. Likewise trading Driftwood for Stone would be a fair deal, but trading Driftwood for Gems would be a rip-off.

Free Level 0: "Rare Goods" (they aren't actually very rare)
Tar Gem Pyramid Stone Mercury Sulfur Jade Diamond Crystal

Resources (Much more valuable)
Mill Quarry Mine
Level 1: Village Driftwood Stone Bronze
Level 2: Town Softwood Sandstone Iron
Level 3: City Hardwood White Marble Silver
Level 4: Royal Redwood Red Marble Gold