How can I stop my lights from dimming when major appliances start up?
Think of the electricity flowing into your house just like water flowing through a pipe.  If you turn on a faucet only halfway then you will probably not notice a drop in pressure elsewhere in the house.  But if your washing machine is filling (or your irrigation system kicks in, etc.) then you will see reduced pressure elsewhere in the house.

The electricity in your house works the same way.  Air conditioners, refrigerators, water pumps, draw a lot of electricity when they first start up and you may see a drop in "pressure" when any of those items turn on:  


  Air conditioners, refrigerators,
  freezers, furnaces, etc. that have
  large motors require enormous amounts
  of power when the motor first starts
  to spin up to speed.  Once the motor
  is spinning, the energy requirement
  drops way down. This instantaneous
  need for motor shaft speed is what
  causes that momentary dimming of your
  lights.
  Reference: http://www.askthebuilder.com/QA_Lights_Dim_When_AC_Comes_On.shtml


As @Tester101 mentioned in the comments, you could look into a service upgrade to your house (which might not be a bad idea) but the problem might also be with your water pump.  The pump kicking on/off every 15 seconds may indicate a problem with the pump itself (capacitor or pressure leak) or possibly an incorrectly sized pump for your usage.  You probably want to look into a new/repair/upgrade of the water pump.