These are from my observations so far:

There are 3 components to your trade income, exports of resources, exports of other goods and a bonus for how long you've traded with a certain faction.

1. Exports of resources are based on how many resources you control. This component of trade, I've noticed, doesn't change even if you add new trading partners. If you have 15 barrels of tea and 1 partner, you export all 15 to that partner. If you have 3 partners, the 15 are divided among your 3 partners.

The one I don't get is how many resources you export. For example, I'm playing UP and exporting tea from Ceylon. However, the number of barrels of tea I'm exporting is larger than the one my plantation says. I'm suspecting some technologies or port upgrades play a part in this. What the modifier is, I can't understand.

For this resource, your income is essentially how many barrels of tea, etc. you're exporting multiplied by the price listed on your trade screen. Furthermore, it seems the province doing the exporting also gains some of it as province income. So you get 2 sources of income on exports, the exports themselves and the tax on them that gets added to province income. However, it doesn't seem to always be consistent.

2. For every trade partner, there's a component called other goods. To me, this looks like pure profit and each partner gets one. I don't think it's divided by number of trade partners so this is a benefit for trading with more trade partners.

In my UP game, I'm exporting a similar amount to all my trade partners. It's generally within 10-20% of each other, no matter how many resources I'm exporting to them. I don't know how this goes up, I'm guessing with technologies and just having the value go up as time passes in the game.

3. The last one is a bonus for how long you've been trading with a certain faction. Each turn, it goes up. Unlike number 2, it seems how many resources you trade to the other faction partly determines how fast the bonus goes up. I don't think it purely determines it, so I believe this still goes up with having multiple trade partners.