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.
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. 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.