When Portuguese first arrived into the Indian ocean, their sailors had the right and every expectation to be allowed the opportunity to trade with the locals, and generally speaking this was respected and allowed. However, especially in those initial meetings, there was a great suspicion and fear by the Portuguese towards the locals, and vice versa. In such conditions Portuguese, both the ordinary seamen and the leaders, were extra careful in how to engage in this trade. Particularly because in the very first port they reached in the Indian ocean - Mozambique - there was considerable trouble with the locals, which escalated into open conflict and Portuguese bombardment of the town.

Favorite solution to ensure safety was simply to not go onshore at all, and stay at the ships and invite locals onboard for trade and negotiations. Upon seeing that it was safe, locals would sometimes in considerable numbers flock to the ships and sailors could trade then and there as they saw fit. Funnily enough, there were more then one instance in which the Portuguese had to remove the visitors as they were starting too loot anything they could get their hands on and get away with.

Even without that, staying on the ships was not an optimal solution, and once in India Portuguese were regularly going to shore. Still concerned for their safety Vasco Da Gama organized a system of rotation where only two to three men at the time (one from each of his three ships) were allowed on shore to trade. In this case if something happened to them that only a few men are affected.

By the time of Cabral, the situation had further escalated, and there were Royal orders by the King himself that people could go ashore and trade, but only after the fleet gets local valuable hostages to ensure safety of their men. The hostage exchange became an important part of Portuguese contact policies, but also a great source of controversy, disagreements and ill-will.

In that same expedition Portuguese set up a "feitoria" - basically a warehouse, ideally a fortress - on shore in Calicut where they could store their merchandise and trade from. After the establishment of this makeshift feitoria in a house provided by the local ruler Zamorin, there were about 50 to 70 Portuguese men in Calicut at a time, again most of them rotating, and engaging in trade. This feitoria was operating for few weeks but was then stormed by locals after growing tensions between the Portuguese and the local Muslim trade. Fifty Portuguese were killed and a handful managed to escape to ships, after which Portuguese retaliated by capturing and burning the ships in the harbor, killing almost all the men on them and then firing on the city of Calicut itself. Portuguese proceeded to the town of Cochin who was more welcoming and with even more scrutiny and rigorous hostage exchanges managed to establish okay trading and diplomatic relations, ultimately using Cochin as their main base of operation until they captured Goa in 1510.

 

As I gave a pretty general overview so far, let's return to the details of actual trade deals by sailors. There is a quote in Vasco da Gama's journal describing exactly this:

In this manner all on board ship went on land by twos and threes, taking with them bracelets, clothes, new shirts, and other articles, which they desired to sell. We did not, however, effect these sales at the prices hoped for when we arrived at Moncobiquy [Mozambique], for a very fine - shirt which in Portugal fetches 300 reis, was worth here only two fanoes, which is equivalent only to 30 reis, for 30 reis in this country is a big sum.

Description is pretty straightforward, the sailors bartered anything they could for trade, even their clothes. Barter in goods was a significant element of trade, especially in low volumes which an ordinary sailor would deal with. Of course it was only an alternative to actually paying in money. And money back then was made of precious metals, mostly silver and gold. By that time period there was also copper coins and Chinese had their paper money as well, but for the trade we care about, gold and silver coins were the norm. And the good thing with money made from gold and silver is that it could easily be evaluated and converted to local currency. Money exchangers who did exactly this were present everywhere, from western edges of Europe to east shores of China and Japan, and it wasn't really a big problem to deal with a new previously unseen coin if it was based on those metals. Find the coins weight and purity, know the value of gold/silver, and you are good to go.

 

Short summation: In Age of exploration sailors could and did go ashore to trade for themselves, under some conditions for their safety, and there they could simply barter what they had or use actual money of gold and silver coins without much problem