Clematis vines can be cut right to the ground and will grow back to be full of foliage and even flowers right to the base. Yet sometimes we don't cut all the way back.
Usually, late winter or early spring, before growth starts for the year. Sometimes we miss our timing and growth has already started when we arrive to prune --- then, we beg the vine's forgiveness and cut anyway. In the case of the vine pictured previously, growing up a wire trellis to a white post. That vine we cut back in fall. Technically that's not a sound procedure since a fall cut back can starve a woody plant. However, the vine is not pretty in winter and pretty is what we want here quite near the family's main-use door. So we take our chances, cutting it back as late as we can work in fall and accepting the possibility that we may have to replant one spring.
Some vines twine, some adhere. That should affect your choice of support. Lattice with all its openings can provide climbing surface for a clematis, which grabs by twining its leaf stalks. However, it is a mistake to attach lattice flush to a wall, as in the previous photos. The eunoymus vine on the left side of the picture can climb because it adheres; it doesn't even need the lattice. However, we had to put hooks into the lattice so the clematis has projections to twine around. To hang lattice as a support for a twining vine, attach blocks to the wall and then attach the lattice to the blocks. This leaves a gap the vine can slip through.