After you can comfortably approach and touch your horse all over with the blanket you can now start the process of blanketing.
Only after my horse is completely comfortable with the blanket do I actually attach it to their bodies. A scared horse can spook and get away from even the most experienced horsemen, and I do not want my horses to injure themselves trying to get away from a scary half attached blanket that is chasing them. If I am not certain a horse can handle the blanket and blanketing process they stay in the barn and or do not get blanketed plain and simple.
Different blanket style require different techniques.
Open Front- Your standard horse blanket has buckles/closures in the front and straps for across the belly. Before I approach my horse with the blanket I am sure that I have it in reasonable order. I generally carry over my on my right arm half folded like the back of your horse with the front of the blanket towards my hand. This allows me gently place the blanket over the back. After it is placed I then attach my blanket in the front first.
Closed Front- These blankets require you to place it over your horse's head like a t-shirt to get it on. Personally I am not a fan of Closed Front Blankets because I find them very cumbersome with tall horses especially when you are short, and are they are hard place on head-shy/ear-shy horses. Not because I do not believe in teaching horses to handle/allow your hands in those areas, but because they do not allow you to release for good behavior when your horse allows you to handle those areas, which is not helpful in the retraining process. But if you do happen to own one you need to put it on your horse like you do your own t-shirts. You don't drag it all over your face and hair, you scrunch it up with the neck hole open and gently place it over your head. I can pretty much guarantee your horse will be better for blanketing if you use the t-shirt approach.
Belly Straps/Bands- Blankets can have up to 3 straps. If there is one strap you should attach it straight across. For two straps you cross them under your horse's belly, and if there are three straps you will cross the outer two and use the middle strap straight across to the other side. If my blanket has a belly band I attach it accordingly. Allow for a hand's width on all straps, they should not droop and hang far below their belly.
Leg Straps- If your blanket has leg straps they can be attached front to back on the same leg or crossed in the center to the other side. All legs straps should be well adjusted and not too loose.