How to get a PIC32 SPI port working for transmitting data?
This application note AN1277 describes how to interface a serial SRAM to a PIC32 microcontroller using the C32 Compiler.  The page has a link to a zip file containing source code, which should have low level routines for reading and writing data via the SPI interface.

EDIT:


  How do I set the baudrate? I am
  guessing it got something to do with
  SPI1BRG


I see that you have downloaded the "datasheet" for your processor (datasheet is a bit of a misnomer, it is 632 pages long), so I will be using page references from that.

The equation (on page 397) for the SPI clock frequency is

Fsck = Fpb / (2 * (SPI1BRG+1))

I believe the PIC32MX360F starts out with a internal FRC oscillator of 8 MHz, divided by 2 (due to the FRCDIV default value of 1 in OSCCON register, page 56), and since you are not making a changes in your code to OSCCON, the SYSCLK value will be 4 MHz.

Fpb is the Peripheral Bus Clock frequency.  It is set up in PBDIV field of the OSCCON register, which in turn is initialized to the value of the FPBDIV field in the DEVCFG1 (boot configuration register), depicted on page 63.  Assuming you haven't changed this, the default POR (power-on reset) value is binary 11, which means the Fpb is SYSCLK divided by 8.

Therefore Fpb = 4 MHz / 8 or 500 KHz.

If SPI1BRG = 1, as in your example, Fsck = Fpb / (2 * (1+1)) = Fpb / 4 = 500 KHz / 4 or 125 KHz.

If your SYSCLK differs from 4 MHz, then scale the Fpb accordingly.

Aren't embedded processors fun?