Answer: Your approach really depends upon the types of weeds you're dealing with, but wintertime is an excellent time to starve them out by covering them with a thick layer of newspapers or weed barrier. If they cannot get sunlight, they will die out. Your other option is to hand pull or dig the pesky weeds out. In the winter, when the soil is damp, is the easiest time to dig. Once you've gotten the weeds out, cover the bare earth with several inches of organic mulch, or with weed barrier and some decorative bark chips.
Aphids are a particularly difficult pest to deal with. I've had good luck using Insecticidal Soap at the first sign of their presence. You'll have to continually reapply the spray, but if you're persistent you can significantly lower the aphid population.
Best wishes with your garden!
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