If it is a clematis from goup 2 or 3 you really don't have to worry (too much) about the weight of the plant, just the trellis itself.
It helps to have a second person to hold the wood in place and ensure everything is straight.
I am not a fan of hammer and nails because I find that screwing is more long lived. If you attach trellis to fence or wooden fence post you need a drill (either electric or cordless) with a small drill bit for use on wood.
You just need to drill a small pilot hole (1.5mm or 2mm diameter drill bit) through the trellis and a bit into the fence/fence post. Choose screws that are long enough to go through the thickness of the batten plus about half an inch to go into the fence post. I use screws that are about 4 or 5mm thick and ideally are galvanized so they don't rust. By drilling a pilot hole it is much easier to drive the screws in straight, cordless screwdriver helps but can be done with a simple screwdriver as well.
Then repeat for the trellis itself to go onto the batten, you may find that the same size screws works.
It really sounds more complicated than it is.
Make sure you plant the clematis about a foot away from the wall and get it to lean towards the fence at an angle of about 45 degrees. handful of bonemeal in the planting hole helps it get off to a good start.
Hope my ramblings make sense, am distracted by Olympics... :)