Use high top boots. Also make sure they have a solid heel. The boots holding up well can be the difference between a successful climb and total catastrophe.
Rig up your climbing rope and attach it to yourself. Do this before putting on the spikes.
Put your spikes on at the bottom of the tree. Spikes are made for climbing, not walking.
Inspect the immediate climbing area. Check the tree trunk (as far up as you can see) for soft spots or thick, loose bark. Be certain there are no harmful insects or other critters that could make climbing dangerous.
Wrap your safety line or harness around the tree and attach it to yourself.
Begin stepping up the tree. Make one step at a time using your strongest leg first. The stance should be slightly toward the face of the tree, not on exact opposite sides. Since you're new at this, don't keep climbing. Just stand on your spikes so you get used to the feel. You'll want to know how the angle of the spikes feel so that as you climb, you will be less apt to make too shallow of an entry. If the entry is not deep enough, the spikes will kick out and that will cause trouble.
Start climbing. Step up stabbing the spikes sharply but take care not to do multiple times on each foot. That will soften up the surface too much. As you go, keep your chest slightly off the tree. As you climb higher, the circumference will get smaller. Adjust your safety line accordingly so you don't get too far away from the trunk.
Practice. Do this near the base of the tree until you build confidence and become more comfortable standing on the spikes. Then it's onward and upward.