First, pace is everything! Like the champion distance runner in the early miles of a race. Others may blow by you on the trail, but just block out their "hellos" and focus on consistent, steady movement.

Second, learn the rest step. On particularly steep pitches, the rest step can keep you moving steadily, though it may seem like a snail's pace. The rest step is a different stride than your normal step. Either increase the length of your stride or shorten it. Sometimes short steps can allow you to get a little rest on the uphill as do long relaxing strides on the downhill.

Slipping, tripping, and falling while hiking?
Lets start with the boots. Don’t be afraid of buying that heavier hard-soled hiking boot. Choose a boot that will allow you drive your heel or toe into the ground. Good traction can be the difference between a fun hardy hike and sliding on your butt!

Here are a few tips will help to minimize mishaps:

Test any rock to make sure it won't slip before committing your weight to it.

Use a trekking pole or hiking stick as a third leg on steep trail for balance.
 

Be particularly wary of wooden bridges and steps. Wood can get very slick in the rain, setting up disaster if you aren't careful of your footing.

Step carefully or avoid wet leaves, mossy rocks, logs, or a wet sloping rock. Shorten your stride and place your boot soles flat with each step to maximize the amount of surface area on which you're walking.