Note! This mission is optional and appears in the journal under various names, depending on random objectives. I'd recommend repeating it from time to time, as you can therefore enrich yourself and "clear" some of Skyrim areas from monsters. You will get the chance to receive this mission no sooner than after finishing the first main College of Winterhold quest, First Lessons.
Find Urag gro-Shub, who should be at the College library, known as the Arcanaeum (accessible from the Hall of the Elements). During the conversation, ask him if he needs your help with anything (first dialogue option - screen above) and you might get sent for search of a random books to a random part of the world.
Leave the College of Winterhold, open the world map and head to the marked area. After getting there, you will unfortunately have to reckon with the fact that the area is guarded by enemies (screen above). During the fight, most of all take care of eliminating the ones capable of using magic and look out for the elite types as they can deal serious damage.
Depending on the type of location, the book can be either on the surface or inside an underground structure. The exact place can very as well, as it might be lying in a well visible place (e.g. on a table) or hidden inside a chest (screen above). After obtaining the book, return to the College of Winterhold and give it to Urag, receiving gold in return.