Best method I have saw comes from BEZ, I did quick search to find his method.
Place the animal in the squeeze.
Rope the nose and pull it off to the side - that will cause the head to naturally be placed in the correct position for the procedure I am about to explain.
Trim the long hair around the base of the horn with a pair of scissors or a clipper. This is the horn that is now sticking up in the air.
Now, using the wire saw you purchased at your local feed store / vet supplies store - saw it off. Ask them for it - they will know what it is. The directions on using are usually written on a piece of paper in the boxand easily followed. Be sure to get close to the head and start sawing. These wire saws are cheap like borscht - so do not worry about the cost - the last one I bought came to a total of almost 4 bucks - handles and all.
The closer to the head the better. If you cut the horn off too long, it is very difficult to get the bleeding to stop - even if you burn it. There are physical reasons for this that I will not go into, so just trust me on this.
When you are finished - you may have a hole through the top of the head that leads into the sinus - for the moment do not worry about that.
Using a pair of tweezers or a hemostat, hunt around the edge of the cut area - when you dig a bit - you will find the ends of small veins - grab them and pull them out - this will stop almost all of the bleeding. If you look closely you WILL find them. There will be a fair amount of bleeding initially which is why I pull out the small veins. Takes only a few seconds to do.
Now that you have completed this operation, you can take a burner - which you just happen to have handy - and rub it around the cut edges of the operation turn the skin black and cripsy - keep the burner moving so you do not fry the head. Make sure you also burn the cut edges of the horn to kill it. It can be a bit smokey when you do this - suck it up if you do not like the smell, because it really does not last long.
Now it is time to turn the head over and do the other side.
In all honesty I usually cut them both off - pull the veins and then let the head lose - and then burn both sides.
Do not be surprised if the animal goes down - just get on with it.
If you want to make it painless you can always inject about 8 cc's of lidocaine around the base of each horn - several locations - about 2 cc's per shot. Keeps them quiet and they will simply stand there while the operation is being completed.
Now for the sinus hole.
All I do is puncture the membrane and leave it. The hole closes in about a month.
I generally give the "keepers" a shot of Pen LA in event of infection.
Give them a good shot of fly repellant and allow them to find a nice dark spot to sulk for a few days. I just throw ours in the bush. But you may want to put them in a barn.
Flies can be a prob, but this procedure keeps the blood down to a minimum and therefore reduces the fly attractions. Believe me we get lots of them here - so pick a time when the weather looks like it will be cloudy and cool for a few days.
If all else fails, call the vet and have him or a neighbour do it - for the newbie who has never been here, that is probably the best way. Watch and learn - then you can do it on your own the next time.
Using the above procedure - not including the lidocaine, I would estimate I could do them both in under 6 minutes total time - you will probably take at least 30 due to inexperience and timidity. No offense please - just being realistic.
A straight gouge and scoop should be done when the horns are about one inch long - fast - easy and a bit bloody. I would probably not go this route with yours.
Do not - repeat - do not use a power saw - it makes them totally crazy!
Any more questions give me a shout.
Bez!