SPI is quite a simple synchronous serial interface in which you have one master and several slaves. There is a clock line and a data line. The slaves have a data in and a data out. The slaves are connected in series. The data out line from one slave connects to the data in line of the next. The clock line is common to all slaves.
The master generates the clock and outputs the data. There are various protocols and data rates. You will have to look at the data sheet of the adc to see which one it uses. Data can change on a high clock cycle, then be latched in on the low transition or vice versa.
The data is clocked through the slaves. So, if you had three slaves to program, you would transmit three bytes, the first byte would end up in the last slave in the chain, the second byte in the second slave and the third byte in the first.
You feed back the data out from the last slave to the data in of the master.
You would have to consult the data sheet to understand the protocol, but to read data from the slave, you normally send a register address to the slave. Then send eight clock cycles to clock the data from the slave to the data in of the master.