For clematis, winter and spring care are important. In the spring, wait until the stems show green sprouts. Then, it's usually a good idea to remove the weaker old wood. Remember, many clematis bloom both on old stems and the new, so don't remove everything. Instead, leave the main stems of the old framework that show sprouts, and remove the thinner smaller stems above them. This way, your sprouts will grow into strong new growth for the coming bloom.
In very cold places (like Vermont, where I grew them for years), the winter kills the whole vine right down to the dirt. They actually "disappear." Then in the spring, they are somewhat slow to emerge, so you must protect the spot, and watch for the shoots. Once they pop up, they grow fast, but beware—they are brittle! If you happen to break off the young spring shoots, it sets the vine back terribly, so it's important to watch and care for the new shoots until they really get going up your post or trellis.
Once that happens, it helps to gently guide the vining shoots as they find their way upward. You can actually "arrange" your vine as it grows, but again, be gentle; the stems remain brittle. Soon you'll see buds, and then suddenly one day, they begin to open. Most popular clematis varieties open incredibly large flowers, often as large as 5 to 8" across. They face the sunniest side of your trellis, and well, just take a look at the photos. Nothing makes a lovelier display.