How does pH affect the initial rate of an enzyme-catalyzed reaction?
This is kind of a broad question to nail down in a specific answer but the initial rate at which enzymes are capable of catalysis will often be determined by the structure of the "host-guest" or "lock and key" area on them, often referred to as the "active site." Enzymes have pH ranges that dictate how active they are; their "optimal activity" can be influenced by the acidity of their environment. When the pH is at an extreme with respect to the proteins in the cell you can effectively "shut off" enzyme activity through denaturation; i.e. the loss of native secondary and tertiary folding reduces the rate at which the enzyme can operate. Temperature can also inhibit enzyme activity in this manner.
If the pH has negatively distorted the shape of the active site (let's say reduced the size and therefore not allowing association of substrate) then it will inhibit the enzyme's ability to affect catalysis and decrease the rate of product formation. Sometimes, the pH can be as such that it will increase the affinity for substrate binding through positive deformations of the active site and will then increase the rate of catalysis.
Not having a specific reaction to talk about kind of makes this explanation vague but I hope you can see the principle behind it. To use an example involving food (and because it's taco night at my house tonight!), pureed or mashed avocados are used in Mexican food and is called guacamole. Exposure of the inside of the fruit to the air causes an enzyme catalyzed reaction with polyphenol oxidase that can be seen as the development of a brown color as the fruit is being broken down into decomposition products. In order to slow this process, some recipes include a copious amount of freshly squeezed lime juice. This use of citiric acid dramatically decreases the pH and effectively slows the rate that the guacamole turns brown by deactivating the enzyme.