I'm having trouble with water getting to my driver side door hinges after rain. I have a small piece of weather stripping that fell of the "angled" portion of my door and the piece that is on the body next to the window looks really bad so I'm thinking this might be the culprit. Any of you replaced this stuff before? I don't know the cheapest place to buy parts of what kind of tools I need for removal/application. How do I effeciently removed the old crusty adhesive left behind on the door from the piece that fell off?

I'm new to the forums so let me know if there's a better place to be asking these kinds of questions and thanks ahead for any useful advice.