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Each meteor shower has a radiant, or apparent point of origin in the sky, and the shower is usually/often named after the constellation where the meteors 'start' from. Simply find the meteor shower for the week, see what it's radiant is, look there in the night sky and start watching. Any place on the globe that can see the radiant should definitely see meteors coming from that direction.
Edit: Think flowers and petals. The center of the flower is the radiant and the petals are the direction the meteors head, literally in every direction from the center.
Edit edit: Even more obvious, think fireworks. The radiant is the point at which the firework explodes, and all the fancy sparkly lights are the meteors shooting out in all directions - the only difference is that the meteors for any given shower only appear to come from a single point in the sky, they haven't exploded out of that point or anything.
Showers vary both over time and between showers, some simply being more active than others, as there's more 'stuff' to go through and so more 'stuff' falling through the sky. The bigger showers should have longer and stronger peaks, and it'll roughly be a case of seeing more and more meteors and then loads of meteors and then less and less before you look for another patch of the sky at another time for the next shower.
Peaks are simply your best bet at seeing something. You can be a day or two out and still see something depending on the shower, but I guess it's like when do you go and see a car show? When the cars are driving to the show and setting up, or when the show is in full swing and open to the public?
