Best way to increase your hiking mileage is to hike more.
Best way to increase your hiking speed is to hike faster.
It takes time.
If you can't hike often because of where you live, brisk walk. BRISK. For as long as your schedule allows. Everyday. Also, just anytime you are going up stairs, power up them. Make the most of any opportunity to challenge yourself. For instance, I have a short walk from an offsite parking garage to the hospital where I work. I either power walk or run it. Its two five minute extra bursts of energy each day. Make the most of those opportunities. We all have them every day, it may be just 2 minutes but make it the strongest two minutes you can.
One or two days a week of explosive intervals. For me, two 45 min spin boot camp classes a week and two 45 minute fast/faster runs get it done. Pushing yourself through barriers -- physical and mental.
Lighten your pack wieght. My summer pack with 100 oz of water is about 12 pounds. Lighter is faster and faster adds up to longer/farther.
I'm with Tim on more cardio, less strength. The only strength training I do is Pilates, 2-3 hours a week with a trainer. Getting deep into those muscles that will stabilize you will help you can go long without strain. I used to weight train but IMHO long strong muscles such as those you get from Pilates or Yoga lend themselves to endurance activities. Totally anectodotal, totally my opinion based on how I feel.
On the food thing, I eat 100-180 calorie power snacks about four to six times over the course of a full day hike. A couple Gu's, one handful of trail mix (approx 200 calories!), one or two Wasa's with natural PB or lowfat cream cheese, a starbucks doubleshot, a Pria 80 calorie bar or two or three. That's IT. I can't eat as much as LRiz because I am nearly twice her age, short and fat. (LOL) I personally don't understand how folks can manage to hike after eating big sandwiches. I'd pass out into a food coma!
I look at a hike as an endurance event with awesome scenery. Food is just fuel for the ride. Too much and excess energy is diverted to digestion.
And finally, mini breaks so the lactic doesn't build up.
Happy Hiking. Happy hikers hike farther.
Find a formula that seems to work for you and keep going. You'll know what works for you if you keep at it and are open to tweeking.
And finally, I am full of $&^^. I know nothing of the subject.