First: They must be free of insects. Many insects are particularly good at hiding. A good spray with the water hose helps knock most off the plant. A good inspection is next; looking in the little joints where the leaf/flower stems meet the main stem. Also, looking at the back of every leaf.
If the plant isn't too large, sitting it in a large kitchen sink or tub is a good place to do this inspection and then turning the plant sideways (with the drain stop in place to prevent clogging) turn the plant almost sideways, dip the leaves in soapy water (a little dish washing detergent in the water works) and then rinse. This washes off pests and a summer's worth of dust. I like to dry the larger leaves with an old soft cloth to eliminate water spots.
There are numerous products sold for making leaves shiny. I've never thought it necessary. Often they make things worse. If you must have shiny leaves, use a little milk rubbed on with a soft cloth.
I encourage re potting plants brought into the living spaces of homes in the winter. By now the potting soil from spring has had the nutrients depleted, some pests hide in the soil and it's a perfect opportunity to inspect the roots for health problems.
Gently turn out the plant with the soil attached onto a tarp or newspapers. Tap the soil ball gently until it starts to loosen. Use your fingers to dislodge the soil from around the roots. Once this is accomplished, gently wash off the entire plant, dip the top portion in the soapy water and rinse.
Make sure the pot you're using has been cleaned with a mild bleach solution and rinsed. I recommend only using pots with drainage holes because a sure fire way to kill an indoor plant is for it to sit in water. This means the pot must have a saucer with adequate sides. Saucer bottoms must be waterproof which eliminates unglazed pottery.
Always have a waterproof protective surface to sit the pot/saucer on or it will certainly make a nasty mark. If you have a lot of plants and aren't too particular about the beauty, a plastic floor protector made to be used under washing machines is perfect (the one without drainage holes.) Simply set the pots in it or put in a layer of river rocks or glass pebbles. If you use rocks/glass, you can keep some water in this to provide constant humidity.
Replant using good potting soil. If the plant had been pot bound, either trim the roots or use a larger pot. Plant to the exact depth they were before.
If you have inside cats, this is where you must cover the soil with either aluminum foil or plastic wrap with holes punched in it to release moisture. Some folks insert clean ice-cream bar sticks so they can't dig/potty.
Some folks will trim their plants back at this time. If you've trimmed the roots, I'd trim back the plant the same amount. How much to trim depends on the variety of plant and if you are preserving or actually want it to be beautiful during the winter months. Some pruning is always suggested to encourage new growth.
The plant will want - demand - the same conditions it had outside. The amount of sun, water, and humidity needs to be similar to their needs during summer. This means extra work on your part especially making sure the humidity is kept at a high level. Using the rock/container is one way and another is misting. Although they enjoy humidity seldom does a house plant want a lot of water.
Watering methods by great gardeners vary. Some will give each a cup full every few days. Others will drench until it runs out the bottom and then let it dry again. If you use this method, water slowly as it will overflow all over the place before you realize you've added too much water.
If you don't have the right light conditions anywhere in the house, you may have to use artificial lighting. This usually takes the display from beautiful to rather functional.
Some plants will survive in an unheated garage or basement as long as they don't freeze and they are neither over watered or allowed to become bone dry. They'll probably loose most of their leaves, not bloom and tend to look pretty awful. Come spring, cut them back and you may be surprised at their growth.
Not all plants come inside and thrive or even live. Until you have experience, it will be taking a chance. But - you have nothing to loose except a little effort.
To spruce up an area with these overwintered plants, place a new flowering plant among them. A poinsettia or basket full of evergreen branches look pretty for several months.
And that folks is about it on bringing in potted plants. Hope all your plants survive and thrive.