Question
Could you please tell me how to rid of worms in my house plant?

Answer
Karen
Without pictures I can only guess what your bug problem is...It could be a centipede (2-legs per segment), millipede (more than a pair of legs per segment), or a larva  of an insect(worm looking)...
Either way the best treatment to prevent them in plants is to water the plants properly...
Bugs in potting soil are a sign of keeping the soil too wet...They breed in wet soils...Let your plants dry out sufficiently between watering.
Water by weight...Put a saucer under the pot...Water and let the plant sit in the excess water for 5-10 minutes...After that time pour off any excess water in the saucer...Pick up the pot...It should feel heavy..Don't water again until it feels considerably lighter in weight...The soil will be light in color/not dark and wet...You can always poke your finger into the soil to see how far down it is wet.
Watering frequency depends on many factors (sun exposure, wind, day temps, etc.)...
You could buy a safer soap pesticide#professionally formulated) and apply it as a soil trench...Read the directions for use as a soil drench..It will kill the worms in the soil..You may need to follow up with another treatment 14 days later. Or if they are on the plant itself (leaves, stems, etc.) spray at the recommended rate on the container of insecticide...

Get to a local garden center/nursery and quiz them on a solution to your problem...Take a sample of the worm in a sealed plastic bag for someone there to ID the problem bug...Buy your products from them and they should be more than happy to help you...
Good luck...
Rick in southern NJ