If the power is not working in a circuit , how do you determine which breaker controls it?
So you have a circuit that seems dead?


Confirm whether the lights work - this shows if its a power cut.
Check other sockets in the area using a known-good appliance or plug-in tester - this helps identify if its one bad socket or the whole circuit.
Locate the breaker box, open, and look for "work in progress" lockout tags.  Could be someone is working on your circuit and failed to communicate.
Sniff.  Really - the nose can be an excellent tool for identifying issues.  Is there a burny smell at any point.  Smell is also a non-contact check.
Look for breakers which are in the wrong position.  Do remember that for various reasons a breaker might be installed upside-down, so read the label and don't go by switch left/right position
Labels - Depending on the age of your install, it may be well labelled, or not.  Read them and look for a label that matches the room you were in.
Fuses - some areas of the world still have fuseable links rather than breakers or cutouts.  These tend to be inside ceramic or Bakelite housings which need to be pulled with some tug to be checked.   Pulling a fuse will stop a circuit, so warn other people, and once you identify a fuse, do label it clearly.


Points not covered, MWBC, US 220V lines, etc.

Lastly, don't ever feel bad about getting a professional to come and do electrical, (pr anything with which you feel uncomfortable)   I personally can't stand plumbing given the possible damage.  There's no shame in knowing your limits.