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Before opening your tube of caulk, press "backer rod" into gaps of a 1/4-inch or more. Backer rod is closed cell foam rope that comes in a range of diameters, from 1/4-inch to two inches. It's costs less than caulk and makes caulking go faster.
Choose a 100% acrylic, eslatomeric caulk, such as "Big Stretch," for both interior and exterior use. It is very elastic, comes in clear and 12 colors, can be painted, lasts long and cleans up with water. Watch this video on how to apply caulk. (LCAN prefers not to endorse a specific product, but this one is a stand-out.)
Use Spray Foam to Fill Bigger Gaps
Gaps too big to fill with caulk? Use expanding spray foam. Once you open the can, it's best to use it all up, so plan ahead. Canned foam is good for insulating water pipe surfaced-mounted to joists or framing in a way that prevents pipe wrap. Remember to note with an indelible marker on the foam, a nearby joist or wall where you've covered a pipe, in case it needs to be accessed. (You can re-expose it with a pocketknife and patch the cut with new foam.)
Install Gaskets on Outside Walls
Unless your walls have been insulated, remove receptacle and switch covers on perimeter walls, insert inexpensive foam gaskets (available at hardware and home-improvement stores) and re-install the covers. They're not usually needed on interior walls.
When it comes to weatherstripping, "you get what you pay for." If to be installed around doors and window sashes, metal products nailed into place will withstand the wear-and-tear of opening and closing for much longer than self-adhesive, plastic products. But certainly use the latter if they're what you can afford and have the skills to install. Either way, pay attention to the instructions: Wind should push the stripping open, toward the door or window.
More Weatherizing Tips
This article and video from "This Old House" offers how-to advice on other ways to fix gaps around doors and windows and in walls. Before visiting the hardware store, take photos of your doors and windows, opened enough to show salespeople which products will meet your needs best.