Okay, I'm going to begin with the very extreme basics here. This page is for people who either rarely hike or who hike alot but have trouble on slippery trails or slopes full of loose rocks. (The mountaineering term for rocky debris on slopes is "scree".) I will assume that you know how to walk on flat, dry ground, but also that you have only been walking around town. If these pointers sounds elementary, perhaps you already know about them. But it's surprising how many people hike often and yet have never given it much thought, therefore never really learned the basics.
The key to walking on slippery surfaces, whether they're covered with ice (frozen) or water (just wet), is to "go with the flow". That is, allow your body to go the direction it is being taken and try your best simply to keep your feet directly underneath. If you try to alter your direction while your feet are still on the slippery surface, you will probably end up with your feet in the air and your butt on the ground. So don't fight it, let it take you where it wants to take you, just work at keeping your feet below you as you move. Worry about changing where you're headed only after you are off the slippery part. If you're lucky, there may be objects along the way to use to alter your heading.
Many people really don't know how to walk up or down steep slopes without slipping. The key is to dig in with your toes or heels, depending on whether you're climbing up or down. When going up, put your weight forward and walk on your toes. When coming down, put your weight backward and walk on your heels. This may be your natural instinct anyway, and it probably doesn't matter much on solid rock. However, you may need to concentrate on it if you're having trouble while ascending or descending in snow or on tricky scree slopes loaded with loose rocks.
When hiking horizontally across slopes covered with loose rocks, the natural urge is to lean into the slope at a parallel angle. This is the wrong method and greatly increases the chance of sliding off! The correct approach is to stand upright, in line with gravity. (Gravity pulls toward the center of the earth, perpendicular to a flat surface, and is not affected by the angle of a slope.) Experiment with this. Stand upright on a short scree slope at a steep angle (20 to 30 degrees) and see if you slide off. Then try leaning parallel to the angle of the slope and see if you can remain in that position without sliding. When you start to slide, simply move back into an upright position to stop.
Over the years, I've noticed that most people carrying a backpack tend to fight gravity and do a lot of extra work as they hike along. People tend to follow the details along the surface of the ground rather than the general trend. If there is a rock or tree root on the path, they will step up fully onto the top of it and then back down on the other side. This means lifting the entire weight of themselves and their pack up and down for every obstacle along the trail, which is unnecessary. It is much more efficient to keep the pack at the same level the whole time. This is achieved by simply keeping the knees bent when stepping over higher obstacles. If there is a rut or small depression in the path, don't step fully down into it. Try extending the toes when crossing lower spots, to keep the pack at the same level.
Walking sticks or hiking poles are the topic of much debate. There are those who swear by them and wouldn't go without them. There are those who say they only slow them down and get in the way. The advantages of using poles are: they can take some weight off the feet, they can act as an extra leg, they can be used to find good foot placement (especially when in the dark or crossing a stream), and they can be used as a balance prop when hiking on uneven terrain. The disadvantages are: they tie up the hands, they get in the way (especially when they aren't being used), and they take extra thought or effort to use (which tends to slow one down). So should you use them? The truth is, it depends mostly on you, the person doing the walking. If you have good balance, you probably don't need them and they probably will only get in the way and slow you down. But if you have poor balance, you probably would gain in stability by using them. Personally, as someone who has good balance, I've never really used them.
Every year far more people die in Alaska from drowning than are killed by bears. This includes saltwater and freshwater, watercraft accidents and stream crossings. The most hazardous part of a typical backpacking trip is the stream crossings, and glacier streams pose the greatest risk. Water levels can rise quite rapidly after heavy rainfall; but they often go back down rather quickly as well, if there is enough time to wait it out. Late afternoon sunlight causes glacier streams to rise, so they should be crossed in the morning, when they're usually at their lowest level.
Glacier streams can move along quite rapidly, especially after a hot summer day, but their cold temperatures and heavy sediment levels are even more dangerous than their high flow rate. High glacial silt content makes streams opaque, hiding rocks and obscuring holes, thereby making crossings rather tricky. The silt tends to gather in clothes and footwear, quickly reducing the buoyancy of anyone out for long in such streams. Due to the cold temperatures, the exposure time involved in crossing glacier streams is of critical importance, not only for preventing hypothermia, but just simply for the ability to keep making progress toward the other side before going numb in the icy water.
Remember to undo the waist strap buckle before crossing any sizable stream. I didn't do this once and almost drowned! (I tripped while crossing a stream, my pack shifted to one side, and I wasn't able to quickly find the waist strap buckle to unclip it. The heavy pack kept my body down in the water, but I did manage to get my head up high enough to reach the surface. I had to do this to get some air a few times, until I finally found the waist strap, undid the buckle, and was able to stand up.) So take my advice and get into the habit of undoing the waist strap buckle.
When crossing a stream, don't waste strength by fighting the current! Try to walk directly across the stream, perpendicular to its flow. If there's much of a current, you may be taken downstream a little, but that's okay. Concentrate your effort and energy in movement at 90 degrees to the flow. It's important to wear footwear that protects your toes and ankles, especially when crossing over a rocky streambed in swift, cold water. Feeling in the toes is lost if they're held in cold water for a while, and it's easy to break a toe. For most Alaskan streams, neoprene booties are recommended, old tennis shoes are okay, sandals are discouraged, and going barefoot is dangerous.
This is another topic of debate, so I'll just list a few methods, the main differences being how everyone holds on to each other and where to position the strongest person. A simple method is for everyone to put their arms on their neighbor's shoulders, forming a line parallel to the stream flow, with the strongest person furthest upstream. Another method is for everyone to hang on to each other's waist (belt or pack), as a long human train facing upstream, with the strongest person in front, and walk across sideways. There's a method where everyone holds on to the same large stick (small log) held parallel to the stream flow. Yet another method (requiring at least four people) is for all to lock arms around the immediate neighbors by holding hands with the persons beyond (two over), forming a chain.
When crossing streams while hiking alone, it's even more critical to pay attention to the safety issues listed above. The simplest crossing method is to just put on your stream crossing footwear and go for it. Many people use a big stick (or hiking pole), both as an extra leg and to probe the streambed for good foot placement. If you lose your footing and find yourself being carried by the current, face downstream and keep your feet out in front of you to protect from running into rocks. If you find yourself getting dizzy or hypnotized by the flowing water, don't stare at it! Instead, remember to look across the water to the bank ahead and focus your eyes on something that isn't moving.