Pilots need to go through a checklist before they take off. Are these procedures decided by the airlines and (or) the manufacturer, or by the Civil Aviation Regulatory Authority of the respective country?
The manufacturer will publish a checklist. Some airlines will choose to use the manufacturer's checklist verbatim, while others will adapt it to their specific operation based on things like safety reporting data from their fleet. The end result will need to be approved by the regulating authority (in the US, the FAA -- specifically the Certificate Management Office or CMO for that airline) before it's used by crews.
An example of how an airline might modify the checklist would be to adapt it in light of new Human Factors research. Telling crews to "run this checklist" during some large interval of time (say, between leaving the gate and reaching the runway, or between leaving cruise altitude and starting the approach) can lead to a missed checklist, and research recommends "anchoring" the checklist to some cue that's unlikely to be missed. So, "run THIS checklist before you release brakes and start to taxi, and THIS checklist when you have about 2000' left to taxi before reaching the end of the runway, and THESE 3 items as you take the runway for departure" gives crews anchor points that they'll observe anyway and leave them less likely to look back and wonder "did we read the Before Takeoff checklist?"
The manufacturer might have made it all one long 15-item checklist that they have crews read "whenever," but the airline could separate out the items that are best accomplished before starting to taxi (knowing that the more items you put here, the longer the delay before the aircraft starts moving), the items that can be accomplished while taxiing (probably not stuff that requires a lot of 'heads down' time like reviewing the FMC routing), and the items that should be delayed until immediately before departure (strobes lights, landing lights, radar etc).
For commercial flights run by carriers or charter companies, the company makes the checklists. These will be based on the manufacturer-recommended checklists.
Pilots working for small companies or flying individually make their own standard operation checklists. Usually when a pilot starts flying a type they will use either a manufacturer checklist or a commercially published checklist. Then, at some point the pilot may make minor changes for various reasons.
For non-normal operations (emergencies), the manufacturer checklists are used verbatim.