Artificial plants and flowers usually only look somewhat realistic when they are first purchased, but then tend to look more fake as the years go by.
One of the main reasons faux flowers and plants look fake is that the colors fade from the sunlight and/or they are dusty and the dust makes the colors look unrealistic.

Here are a few options for cleaning silk plants and flowers to make them look more realistic for longer.
 
Traditional Dusting
The most conventional way to clean artificial flowers and plants is to dust them the same way you dust everything else in your home, except do it outside.
Take your faux plants and flowers outside and give them a little shake to shake off some of the dust. 
After that, wipe them with a rag or feather duster.
If you want to use a slightly damp rag or a dusting solution, make sure to test it in an inconspicuous place to make sure it does not discolor your silk plant or flower before cleaning the whole thing.
 
Compressed Air
Another option for cleaning artificial plants and flowers is to use compressed air or a hair dryer on the cool setting. 
Take your faux plants and flowers outside and spray them with compressed air or your hair dryer to remove the dust.
You can find compressed air in the computer department of most stores or you can use an air compressor. 
Ammonia Cleaner
Consider using an ammonia based cleaner (such as window cleaner), plain water, vinegar, or dishwashing liquid on silk flowers and plants.
All plants are different, so test them in an inconspicuous place to make sure it does not discolor your plant or flower before cleaning the whole thing.
 
Plain Water
If your plant tolerates water, you can wash it in the kitchen sink or spray it with a garden hose.
 
Vacuum
You can use a vacuum to clean your artificial flowers and plants and remove the cobwebs and dust.
Use a vacuum attachment with a brush so you don't pull the leaves into the vacuum. 
You can even use a small hand held vacuum to clean your silk plants and flowers