First thing to do anytime you see such unnatural thing on your plant is to try to get rid of it.
The most often remedy first tried is with the use of water.
Take your plant to where you can spray indiscrimately a stream of water at the plant. I say AT, instead of "on", because that is what will knock off most pests.
Once off, they don't come back....at least, not that pest, but their offspring may already be ready to jump aboard.
Pests that invade our plants usually have strong parental genes that causes them to look to their young.
Some pests have very short gestation period...as few a few days to a couple weeks. Your plant may be, right now, harboring the eggs, or the larvae of the specks you see.
The soil your plant is in is most likely to be where the next invader is.
Any treatment you give, must be repeated in an attempt to break the cycle of the gestation period.
Usually, application of a treatment can be done 3 times within a short period...usually 10 - 20 days.
That is, treat today, in 5 days time, and again 5 days later. This often will break the cycle...but continued vigilance must be done.
There are many remedies suggested to rid plants of what invades. Sometimes it can be as bad treating the plnat as letting the little buggers have their way.
Know what the pest is before treating.
Water is not going to harm the plant, so make that your first thing to try.
Soap and water is another treatment that can be tried in most instances. Soap--like it lays on your skin, dries out the skin of the bug. Soap will interefere with the bugs breathing; all bugs are air breathers.
One such solution is 40 parts water, 1 part dishSOAP...(not detergent) sprayed on the plant from top to bottom, bottom to top, making sure all surfaces are treated, then wait for no more than ten minutes before the plant is thorughly rinsed with clean water, top to bottom, bottom to top.
There are bugs though that are not affected by this; they might have a hard shell that soap does not do anything to.
For these, there are other measures to try.
One is the use of dormant oil---the same oil that is used on your outdoor trees, shrubs and roses, in the spring.
Then there are the insecticides, pyrethrum, rotenone and others that you should tread carefully with--they are poisons and should be used only when all else fails.
Sometimes, if you feel eggs or larvae or pest themselves are in the soil, you can immerse the whole plant over the rim of the pot until bubbles stop, telling you all cavities are filled and the bugs will be forced to come to the surface.
On store shelves there are many insecticides that might list treatment for a bug you have identified.
Again, treatment should be repeated to break any cycle the bug might have.
Further reading about the use of baking soda, sprinkled on soil, can be done.
Identifying a bug and then doing a Google search can often advise owners how to treat.
If you can see the pest, you might be able to be rid of it by simply scraping them off. Put a leaf into the palm of your hand and carefuly wipe with a tissue. Or dip a Q-Tip into a bottle of rubbing alcohol and touch the pest with it.
But leaves are not the only place bugs hide. They get into the crotches of stems/leaves, or they invade the leaf itself, eating their way through and out.
Or they can be found in the petals of flowers--and this can be tough to treat because spraying a flower is not recommended simply because most times you will harm the bloom.
Water spray might dislodge the pest or make it more visible. In any case, do read about the pests and this can be done in most cases simply by buying a book or pamphlet on the care of houseplants.
These books are widely available in books stores --but try a USED bookstore first; gardening books are always there at very reduced prices.
Eventually they gotta breathe, and when they do there's water being pushed inside. They drown & die or get blasted off and go down the drain.
. 
-Dodge
