Use a checklist.
Ask questions. Ask everybody. Mechanical staff, or engineers, or what ever you call them, make their daily bread inspecting and are a bonanza of knowledge if you can get them to share. Read tech publications, if you have time. There's a gozzillion looseleaf manuals on hand in the maintainence office. Mostly way too much deatail for a pilot's pointy head, but some are quite informative (and have pictures).
Use a checklist.
Use a checklist. I'm guesssing the one supplied isn't adequate, so take advantage of the computer age and word process your own. Update it as often as you can. Suggestion-the small heavy paper lose leaf binders, or what ever you call'em, with the flexible tabs will hold and protect a dozen or so pages and drop right into your chart bag...
Use a checklist.
I won't fly anything that I haven't preflighted, unless somebody I trust has done so. Perhaps that's why your instructor hasn't put more effort in?
Use a checklist.
Finally, I won't fly with anybody who doesn't at least walk around the bird before strapping in.