I'm specifically wondering about the situation in which there are no native settlements around that could trade food or information about the land. How did they act? Were they left to completely fend for themselves or could they expect to have supplies regularly brought to them? Would knowledge about fauna and flora from back home help devise survival techniques or would colonist be afraid of interacting with their surroundings?
The question applies to anywhere around the world. North and South Americas, Africa, Oceania, some island in the middle of the ocean, etc.
Finally, is there any known and well described case that I could read about?
Even a proximity to native settlements to trade with is no guarantee for consistent food supply - the Jamestown colony depended partly on trade with the local Powhatan settlements, but when their own crops failed and the resupply ship from England got delayed and arrived only with new settlers, and no new supplies, the situation got increasingly desperate. The colonists weren't used to farming, and quickly exhausted the supply of game in the area, and their access to fresh water was poor.
This ultimately resulted in what is called the "Starving Time", which lasted the winter between 1609-1610, and was so desperate that some of the colonists even resorted to cannibalism. When the colonists abandoned the colony, they had been reduced from 500 people to merely 60.
Clearly, the Jamestown colonists were unprepared for their crops failing, and had chosen poorly when picking a place to settle, at least in terms of access to fresh water. How true this is of other colonies in North America, I don't know.
Stuff You Missed in History Class has done an episode on Jamestown, with a good list of sources. Cannibalism in Jamestown