SPI speed connection

I am using an arduino mega and a W5100 ethernet module. I would like to know how I can determine the communication speed between the arduino and the module.

Do you mean actual amount of data per second or the frequency of the SPI bus? You can probably do some totaling and dividing by time if you want actual transfer speed, or view it on your router if you have the W5100 on your home router. For SPI bus speed, it's probably the default, I think there is a default 4000000Hz or 4MHz in the SPI.h but the library you use to drive W5100 can use a different speed for each transaction. So you can look into the library for SPISettings() to determine what SPI frequency was used.