You use int 0x13 to load in the required number of sectors and jump to the location you have place the new code. There is nothing you need to do in the second stage, but you will want to make sure that you set DS to be valid for wherever you load the code.
Example from my little OS archive:
/* BIOS loads the sectors into es:bx */
pushw $STAGE1_WORKSEG
popw %es
movw $STAGE1_OFFSET, %bx
read_stage1:
/* Try to read in a few sectors */
movb $0x2, %cl /* Sector */
movb $0x0, %ch /* Cylinder */
movb $0x0, %dh /* Head */
movb $0x0, %dl /* Drive */
movb $0x2, %ah /* BIOS read function */
/* How many sectors to load */
movb $STAGE1_SIZE, %al
int $0x13
jnc read_stage1_done
/* Reset drive */
xorw %ax, %ax
int $0x13
jmp read_stage1
read_stage1_done:
/* Perform a long jump into stage1 */
ljmp $STAGE1_WORKSEG, $STAGE1_OFFSET
call halt
halt:
/*
* Function: halt
* Synopsis: Sends the processor into a permanent halted status
* Notes:
* The only way out of this is to manually reboot
*/
hlt /* Halt the processor */
jmp halt
That's in GAS format so you'll want to reverse the operand order because it looks like you're using NASM from the times instruction. The variable names should be self-explanatory.
If you're developing a hobby OS then http://forum.osdev.org/ is a good place to get support from others doing the same thing. It's a bit more specialised than stackoverflow and a lot of OS stuff can be quite esoteric.