The way I do it is to wrap each horizontal wire around the post and then around itself 3-4 times. Depending on the wire type, often at the start of the roll there is a foot or so of extra on the horizontal wires, which makes it easy. If there isn't it's usually enough to cut along the edge of a vertical stay which gives you enough wire to work with. At the starting end it's important to be careful to keep it even, which means fastening at the top, then the bottom, then the middle, and working your way along keeping it even. I typically use 48" fence with 4" spacing so it has 13 horizontal wires, it's a pretty good job to do 13 ties. Once the wire is tied you want to keep it from sliding up and down on the pole, the only way I've found to do that is to drill a hole and run a short piece of wire through.
The other end is trickier. What I do is put the pulling point at least six feet past the post. Then one at a time I cut the horizontal wires and wrap them around the post onto themselves. In order to get them to go around the post I cut the vertical stays starting at where the wire first touches the post up to where the horizontal wire is cut. I cut the horizontal wire longer than I think I'll need and then cut it when I'm done. I used to untie the knots where the vertical stays join the horizontal wire for a neater look, but it's less work just to cut the stay and leave the knot, and I believe the knot creates friction which helps the wire stay on the post. The key at this point is maintaining tension, so I do one wire at a time and try to tie it as tight as it was before it was cut. I do one in the middle, then one near the top, then one near the bottom, then keep alternating and to the top and bottom last.
To get tight ties you need a wire twisting tool. I sometimes use this one: Amazon.com : Zareba HTTT Wire Twisting Tool : Outdoor Decorative Fences : Patio, Lawn & Garden
but my favorite is the Fence Pro: Wrap t-post clips tightly without pliers - No hand strain or pain
If you aren't satisfied with the tightness of the fence after tying it there is a tool that looks like a pair of plyers for deepening the crimps which will tighten it up.
Wear eye protection when doing this. It's hard on the hands too, I often find myself icing my hands after a day of tying fence.