Your adventurers don't spend all of their time adventuring. This holds especially true if you are running the game the way it was intended (1 day in real life = 1 day in game time while not playing).
Downtime is what your characters are doing outside of adventures. In order to perform downtime successfully, your characters must end each night being able to Safe Rest.
Note that although the downtime rules apply to all tiers of play, once characters reach Paragon Tier (Level 10 and higher), there are optional additional downtime rules for running kingdoms, holdfasts, strongholds, temples, or anything else your character ends up being in charge of.
However, these downtime rules continue to apply to characters of all levels while adventuring, or performing specific tasks (such as preparing 3rd Circle Spells).
Characters should be allowed to do whatever they wish during downtime. As such, the GM should be ready for characters to do things outside the scope of the rules, and the GM should be ready to help the character walk through it.
The GM may use existing rules as a guideline, or simply come up with something that works for what the character wishes to do. Often times, your character will just be living.
Sometimes, characters may wish to do something dangerous during downtime. GMs should strive not to kill a character during downtime, unless the task is sufficiently dangerous, and that the possibility of death is discussed ahead of time.
If the PCs attempt something dangerous during downtime, seek other forms of adjudicating the story beats generated by such an interaction. Here are some ideas:
If death is unavoidable, players and GMs should work this out ahead of time, and players should understand what they are getting into.
Keeping track of downtime is perhaps the most difficult part. As a GM, you should be keeping good time records for the players, and as players, you should try to be in communication with the GM between adventures, as often as possible when you wish to change course.
This is especially true when you wish for your character to perform during downtime. And becomes even more important when your character wishes to spend much of their downtime performing tasks for which they may require multiple breaks between.