Trading is an important element of the game. To gain the best edge on your competition you must learn to trade quickly and efficiently.
1 Port Features and Filters
2 Trade mechanics
3 Article Shuffling
4 Friends + Port Resource Dump
1. Port Features and Filters
You can choose to view either all resource trades or only those with a favorable ration (1:1 or better)
Listed trades are sorted in order of proximity to your city
You can filter by the type of trade you are looking for and in what amounts you are looking to trade
This should allow you to quickly find the most useful listings available without having to scroll through dozens of pages in the hopes of finding something.
2. Trade mechanics
Outside of the Port you can manually send a maximum of two trades to the same player in a day. That is two Agreements or two resource loads at maximum capacity.
Furthermore, you are limited to six total trades in a day regardless of who you send them to (again these are direct trades not Port trades).
Finally you are limited to an exchange of 50,000 resources per week with a player (in one direction). However, if the other player sends resources back (perhaps of a different type), that frees you to send more than the 50,000. You simply cannot have more than a 50,000 difference between your trades. Raided resources count against this limit. So if you were to raid someone for 50k, they could not also send you resource trades. Sorry folks you can't collect ransom on top of your raid take if you max it out with the raid.
The 50k limit is a soft max, the hard max is 100k in situations that would cause you to go over. The key point is that if you are at the 50k limit, the game will not allow you to send or receive (depending on which direction you have reached the limit) any more resources. See the galley trick to increase raid returns.
3. Article Shuffling
You already know you can manually trade 2 articles with a player outside the Port. You can of course scour the Port for the article you need, but what happens when you come up short?
Lets assume you are trying to discover Stymphalos 3. You have #1, #2 and two #4's but no #3. You also don't see any listing for exchanging a #4 for a #3. You do however see a listing asking for a #4 and giving a #2. Your next step should be to check the listings for #2 and see if there is a #2 for an #3 exchange. If you do then you can chain your trades accepting both the #4 for #2 and the #2 for #3 listings. This will use up two galleys but when all is done, you will have all four referrals and can sign the Agreement with no spares left over. You can likewise trade one type for another type if necessary, but due diligence can see that you rarely if ever are stuck with a duplicate past Article.
If you do get stuck with a duplicate, then you have three viable options.
Give it to a friend.
Sell it via the Ephorate
List it for a higher Article (You might get lucky).
4. Friends + Port Resource Dump
As always galley travel time between friends is 24x faster than normal. If you have a close friend, you can easily trade all of your resources to them fairly quickly without running into the trade limits listed above. The way to do this is to make a listing at a 1:2 ratio that no normal player would generally accept. You then have your friend (who will see the listing at the top of their list) accept the trade and wait till the trade completes. You can continue doing this as long as necessary, switching between resources until you have emptied your coffers. If you have max galleys and your friend is a minute away, you can transfer resources at a considerable rate every two minutes. This also doesn't necessarily have to be done as a last minute dump, you can use this method as a matter of course to save your real galleys for instances that don't allow you to go through your friends.