Question: There are two worlds of more or less equivalent technological level, say a difference of only a few decades and no more than 50 years. A first contact event occurs and after the hoopla dies down trading starts. 

Initially, barter is the primary form of trade but this quickly becomes cumbersome.

How would the two economies first establish a currency exchange and exchange rate?

Some commodities are similar and occur in similar quantities, particularly minerals gold, iron etc. Other commodities are unique to one civilization or the other; plants and animals unique to each planet, unique tech developed by one and not the other.

Some restrictions:

* Both planets have one currency or at least a dominant currency (like the USD)
* Neither planet is in a "dominant" economic or technological position.
* Travel between the planets takes a few days
* There is a moderate level of trust in business dealings but it is not clear how laws apply to off worlders on each planet.

Ideas I've toyed with:

* comparable commodity-based exchange, ie. gold standard type exchanges, but this seems archaic for technologically advanced worlds and would anyone really want to transport heavy gold out of the gravity well of a planet
* some type of crypto type exchange, but this seems problematic with distance and not very conducive to trade as the price fluctuates

Answer: 
Comparing commodities. Money, after all, is just an abstract representation of goods and services. The only reason any form of fiat currency has power is its ability to be swapped for either a good or a service. A way to get an idea at what the exchange rate would be is to just compare a common and frequently used commodity between the two and use it to set a benchmark.

The trick is finding the commodity. Any metal that's used in equal measure would be useful, but suppose one planet is iron-rich and the other is iron-poor? Or perhaps one culture values gold whereas the other values silver? If both planets have the same amount of metals and use similar ways to process it, that would be the best, but that's not always the case.

Services would actually be another good place to start. Figure out the 'living wage', as in how much money would be the bare minimum for living expenses i.e. food, clothing, shelter at a minimal level. Or plot a graph with the respective salaries for necessary jobs - like doctor, farmer, lawyer, etc. (Cue lawyer joke.) Take all that information together and you should get a pretty good idea of what the exchange rate should look like.
**I think the short answer is: you're missing a step.**

**The next step in that picture *isn't* a currency exchange. If you've got a trader who's currently taking barter in exchange for their goods, the next step is to *take the local currency instead.*** Instead of taking on 500 kilos of sodium chloride in payment, you get 500 cilrish - which you know you can use to purchase X, Y, and Z at the local alien freemarket. There isn't an exchange rate - you're not directly exchanging dollars for cilrish. In fact, the trader in that situation doesn't even really care about an exchange rate. Instead, they care about the goods X, Y, and Z versus the amount of dollars they spent on the venture. The trader may even keep spare cilrish - but mostly from the standpoint that it'll let them buy goods on the alien planet.

So for small-time trading, there isn't an exchange rate. But what happens when trading gets more prevalent - or, more directly, entities start springing up that do *one directional trading* - they focus on importing A and B from the alien planet and selling them on earth. In that case, the business needs to find a way to convert dollars into cilrish.

But there are likely business entities on the alien planet with the same problem. They're importing Miniature Corgis (a delicacy on their planet) and receiving payment in cilrish... which those businesses have to convert to dollars in order to purchase more inventory.

At that point, there's still not really an 'exchange rate', so much as a "Here's a rate we happen to agree to a transaction to at this point in time." It's just two companies agreeing to swap X dollars for Y cilrish.

Now, once there's a *market demand* for exchanges, that's when an actual exchange rate pops up. Because there's enough trading of cilrish to/from dollars that an actual proper rate can be established.