Advice I have after many years of hiking (in no particular order)
Carry twice the water you think you will need and bring high fat and high protein foods (chocolate, nuts, beef jerky, etc.)
Wrap Duck Tape around one water bottle, it fixes everything and can be used to wrap blisters almost as effectively as moleskin.
Carry a knife, compass, map, flashlight, watch, GOOD rain gear (cheap stuff is hot and sweaty), zip lock bags (to keep personal items dry), trash bag (to keep back pack dry), cell phone, maps, bivy sack, and a spare pair of socks (Smart Wool is great).
Leave your plan with someone that cares if you disappear (Ex's not eligible)
Pack the tips of your boots with a paper towel to prevent foot sliding on descents
LEKI POLES ARE GREAT!!!! I hiked on bad knees for ten years with debilitating pain at the end of major treks, I always pictured Leki poles went with the Fifty year old + crowd. I use them religiously now and they make the descents a breeze. Since using them I haven't felt a twinge in my knees. Just make sure to stow them on vertical ascents or descents.
Pack warm clothing and avoid cotton in the winter, it looses its insulating ability when wet whereas wool and synthetics do not.
Check the weather for trips as well as the conditions of the roads leading to trailheads.
Make yourself aware of potential hazards (lightning, animals, bad trail conditions, etc).
Caffeine and plenty of liquids help with headaches from altitude sickness.
Break in your boots, 25 miles or so is a good rule of thumb.
Don't overestimate your physical condition, real hiking and climbing requires good conditioning, you can find yourself out of energy in dangerous places if you bite off more than you can initially chew.
It never hurts to have the phone numbers of ranger stations programmed in your phone.
Know a little first aid, if you have the time, know a lot.
My wife suggests toilet paper if you are a female hiker, baby wipes also come in handy.
In the mountains ALWAYS bring your ice axe, I have needed it more times than I can remember.
Start all hikes early, plan to be off summits by 11:00 if possible.
Don't be afraid to turn back from a trip, there is always tomorrow.
The only way to become more competent is to always push just slightly outside of your comfort zone.
Research all routes as thoroughly as possible.