There are a few ways to skate forward, some techniques are better than others, but ultimately there is one technique that is the most effective when skating forward.
When you first want to stand in the hockey position (image on far left). From there, you make your feet into a v-shape. Now as you take a stride, you want to extend your leg while the same-side arm extends forward. When taking the stride you must keep your back as straight as possible.
Once you've completed the stride you must bring the leg and arm back into position like the image on the far left. Once you are back into position you do the same thing to the other side and it will go back and forth.
Here is an example of me skating during one of my hockey games.
Snow Plow Stop
For beginners, a simple way to stop would be what's called, the "Snow Plow" stop. This also ties in with skiing as you point your toes towards each other while bending your legs to slow down.
In this action you will feel awkward but make sure you are bending your knees so you don't fall forward onto your face.
Regular Hockey Stop
For more advanced learners, a regular hockey stop is more difficult. However, there are ways to make it easier.
When stopping, for whichever side you would need to face whichever way you stop. For example, if you were to face right you would lift your right foot up and use your left foot to face towards the right and once your left foot is back down you could put your other foot down as well facing the same way. When you want to face the left side you would lift your left foot up and use your right foot to turn towards the left side and once it's facing that side you could put your opposite foot down facing the same way.
To make it more challenging and what would be more common as you become better you would face both feet simultaneously whichever way you want to face. In this case, it would not be one foot at a time. Instead, you would glide a little while stopping.