Pages 19-21 of the AD7873 datasheet tell you all you need.
You can either bitbang the required data, or as it is apprently SPI-compatible use an SPI module of your microcontroller to send/read the data if it has one.
Basically you send an 8-bit control word with the bits set accordingly to the operation you want the chip to perform, and you then send 2 more dummy 8-bit words (contents arbitrary as long as the START bit is not set) in order to read the response.
Find yourself some SPI bus docs to get a more general background over how it works.