"Training" per se is mostly done by reading forums. Many companies do some training or certifications for jobs. All provide specific job instructions--some better and some less than wonderful.
Over time you will come to do some things automatically:
Remember where you parked
Look at the stores to the right and left of the place you are shopping
Note the condition of the parking lot, landscaping, building, signage etc.
Note obvious trash or pedestrian/vehicular hazards in all the above
The time you entered
A restroom visit
Cleanliness and order of the establishment overall--stocking, quality of signage, cleanliness of floors etc.
The name and description of the person you interacted with
That you have the receipt or proof of visit in hand before exit
The time you left
Anything beyond this is shop specific. That is what you scan your job instructions for and you look over the questionnaire for. The more of the basics that hit your 'autopilot' the less specific information you need to remember job to job because the stuff has already become a habit.
Whenever I tackle a new-to-me job there is a cheat sheet in my pocket. Today's new-to-me had 'Pick 2-no bev','nutrition', 'line to deliver', 'take out menu' because these were the only unusual items. Although the questionnaire didn't ask, I can tell you from 'autopiolot' training that the parking lot was in excellent condition, the building well maintained, there was no trash and the building was free standing with __ street on the right and the parking lot of ___ on the left.
The other 3 shops I did today are ones I have been doing for years that require no cheat sheet. Autopilot takes over entirely on these and I just make some notes as I go so I make sure I visit all 7 required stations and have my coded notes ready to transcribe onto the report which at first took close to 20 minutes to complete but now is so automatic that it takes around 4-5 minutes.
In many stores you can use a 'shopping list' type paper to make notes or review what you need to do. I find a scrap that looks like a shopping list works best and do indeed check off stuff. I find it useful to look at a display then look at the paper as if I was writing notes about the item (price, etc.) If my note is more than a couple of words, I may handle a decoy product, looking at weight or ingredients before continuing my note taking. My favorite 'shopping list' scrap is a small spiral note pad.