Beth, you really should know what the insect is before attempting to treat it. Many insect issues can be treated with no more than a good, commercial insecticidal soap. I don't recommend "home brews" because no one has tested the ingredients or the quantities.
Up here in Canada we have a gardening guru who has a recipe for a solution of 1 part dish soap to 40 parts water...put in a spray bottle, mist your plants thouroughly (ie under the leaves as well as the top of leaves) let stand for 10 mins & rinse thouroghly. I just had a war with spider mites & it worked like a charm!
As Doug says check out what insects are on your plants as some feed off others but I do not like aphids on my roses so I spray with garlic water just made up of either fresh crushed or powder in boiling water.Leave to stand over night and then spray.