Answer: Liriope is semi-evergreen or deciduous in your area -- you are in zone 5 which is a bit cold for liriope. In the spring before it begins to grow again, trim it back to remove the discolored foliage. You can probably set your lawnmower on high and use that if you have a large area to cover. Be careful not to damage the new growth coming up in the center of each plant.
Potentilla shrubs are routinely trimmed in the early spring to remove winter damaged tips and restore a symmetrical look to the plant. After the first bloom flush you can shear it lightly to remove the faded flowers and encourage rebloom.
Weigela probably will not need pruning for several years after planting although you may want to trim the occasional overly long, wayward tip. The time to prune is right after it blooms. About year four, begin removing up to a quarter of the oldest branches by cutting them off at the bottom of the plant. This will encourage vigorous new growth while maintaining the natural shape of the shrub.
Most hollies do not require pruning and have a very regular natural shape and form. Pruning will interrupt the cycle of flower bud and fruit development, so the only pruning you would do is to remove a broken or damaged branch. You may want to provide it with a windbreak every winter and consider using an antitranspirant spray to try to protect it from drying out. Also, if there is a heavy wet snowfall, sweep or brush the snow gently off the branches to keep them from breaking under its weight.
Clematis pruning depends on what specific kind of clematis you are growing, but none of them would be pruned now in the fall. Here is information on growing and pruning clematis you may find useful. You may need to cut and paste the complete url into your browser to make it work correctly.
All of the above will benefit from a year round layer of organic mulch several inches deep over the root area. Apply it in a flat layer and do not allow it to touch the crown or stems or trunk of the plant. FLuff and replenish the mulch as needed to maintain that depth. In the late fall you could add to it, making it up to six inches deep, but do not cover the plants. In the spring gradually pull the excess mulch aside to help the soil warm up faster.
I hope this helps.
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