Eliminate whatever is attracting the insects, and they may soon leave your home. Clean often to keep areas dry and don't leave trash or pet food lying around. Insects are often a symptom of a larger problem: unsanitary conditions.
Seal cracks on the outside of the house where insects are entering with a caulk gun. Bugs such as ants and cockroaches typically find a way in by crawling through these cracks in your exterior.
Use ordinary insect sprays you can find at the grocery store for minor nuisance insects, such as the occasional roach or spider. These sprays only deal with superficial problems, however, as they don't penetrate deep into areas where insects are living.
Spread boric acid -- which you can find at most retailers and hardware stores -- around areas where you see a lot of insects. Boric acid, which acts as a stomach poison, is particularly effective against roaches, termites and ants. The substance is a "green" or natural alternative to other household insecticides.
Call an exterminator if you have a deep-rooted problem or large colonies of insects. A professional will be able to determine exactly where the insects are coming in, where they're living and what the best solution to the problem is. They are also certified to handle dangerous chemicals that you may need to deal with the problem.