"READ SEQUENCE (READ): Reading the AT25HP256/512 via the SO pin requires the following sequence. After the CS line is pulled low to select a device, the read op-code is transmitted via the SI line followed by the byte address to be read (see Table 10). Upon completion, any data on the SI line will be ignored. The data (D7–D0) at the specified address is then shifted out onto the SO line. If only one byte is to be read, the CS line should be driven high after the data comes out. The read sequence can be contin- ued since the byte address is automatically incremented and data will continue to be shifted out. When the highest address is reached, the address counter will roll over to the lowest address allowing the entire memory to be read in one continuous read cycle."
So you send a READ command (0b0000X011) and a two-byte address (0bXaaaaaaaaaaaaaaa) and start pumping out data.