Is this a hinged door or a slider?

No expert here, but we had a similar water issue with our deck. Your threshold needs to be higher than the patio or deck. If it is not, maybe that is the problem.

Pictures?

It could be many issues. With no specifics, there will probably not be many helpful answers.

Is the water coming in from the bottom, the sides, or the top? Is it leaking in around a glass? Is it making the floor wet, or the wall board wet, or what?

What kind of door is it? A storm door, a solid door?

Is it under an overhang, or exposed to the side of the house? Is there a concrete patio or a wooden porch, or deck, or what outside the door?

Is it an old door? Is the door warped?

Could it be that you might have a clogged gutter that is allowing water to cascade down the side of the house and come in through the door? Maybe?

Without some details, it is anybody's guess.

Your bug problem and your leaking problem may, or may not, be related.