Welcome to ATP. Hope we can help you here. It would be helpful to us to know your location, what kind of plant this is, and is this plant indoors all year round? You can put your city, state or country into your personal profile. A picture of the plant is also a big help.
Usually there are microscopic eggs on a plant that start up the infestation. They can be on the undersides of a leaf, or on the soil and suddenly you have a million . . If you put your plant outside in the warm months, well you can expect to get any bug or fungus on it.
Anyway, the best and simplest remedy is simply spraying the plant with a soapy water solution. About 1/2tsp. of dish soap to a quart of water in a spray bottle, and spray the plant thoroughly, including the stems, soil surface, and upwards to cover the undersides of the leaves where the little monsters breed and lay eggs.
You should do this treatment at least two or three times in the course of a couple of weeks, to be sure of killing off all the generations of mites. I like to rinse the plant off with clean water the day after I treat with soap as well. If it's too cold to take it outdoors and use the hose, you can put it in the kitchen sink and spray it, or take it into your shower. If you're worried about over-watering when you do this, cover the soil surface with plastic wrap or tie a plastic bag over the pot to keep from soaking the root ball. Depends on the type of plant but most indoor plants love to be showered.