Pinhead,
The procedure for Cabin Alt warning horn requires Oxygen on,, establish crew comms, manual mode, valve closed;
THEN an assessment of whether or not the cabin altitude is controllable. Some tinkering may be required at this point.
The most important actions when the CABIN ALTITUDE WARNING goes off are, oxygen on 100% (for obvious reasons), establish crew communications (so you can make a joint assessment of the problem).
The majority of in service pressurization problems are controller faults, and in the NG these are rare, but there is a good chance that if you take your time you will regain control of the cabin.
The majority of SIMULATOR exercises are faults designed to force you in to an Emergency Descent, to tick that box..... But depending on the syllabus or the fault induced by the TRE, you might just avoid all the drama if you take the time to assess things. This can be done with you Oxygen mask on after the horn has gone off.
The humble and honest account given above by Tee Emm is a great example to learn from.
Cheers