So I just got back from skating, and I figured I would do a video on a basic On-Ice warm up. I decided not to do too much of a written tutorial because it's kind of hard to explain, so the written one is less detailed than the video.
First, before you put on your skates, roll and stretch both of your ankles. Next, when you're on the ice, do a lap in each direction. When you're done with that, go to the boards and stretch your thighs, hips, and hamstrings most importantly (Exact stretches show on video). After you're done stretching (hold each stretch for 10 seconds at least), start with some basic footwork like edges and three turns, then basic jumps (Waltz jump, Salchow, etc.) and basic spins (one foot spin, scratch spin, back spin, etc.).
You should be fully warmed up! For cool down, I don't usually stretch (even though I probably should), but I do a couple slow laps around the ice.
My life on ice: Warm up tutorial