Get/Swap Array Elements in MIPS

Question

I am very new to MIPS and this is a homework assignment, so I'm really just looking for a clue to get me going. :) I have looked around for similar questions but didn't find anything that was what I needed, so I'm sorry that this has been asked before. I am writing a bubble sort in PCSpim, and I think I am pretty good with the code, except for swapping.

Here is the pseudocode:

lastUnsorted = length - 1
sortedFlag = 0
while(lastUnsorted >= 1 and sortedFlag == 0) do
   sortedFlag = 1
   for test = 0 to lastUnsorted-1 do
      if(numbers[test] > numbers[test+1] then
        temp = numbers[test]
        numbers[test] = numbers[test+1]
        numbers[test+1] = temp
        sortedFlag = 0
      end if
   end for
   lastUnsorted = lastUnsorted -1
end while

I think it involves getting the addresses of each element, checking to see if the first is greater than the second, and completing a swap via a swap function. Here is what I have:

            .data
numbers:    .word 20, 30, 10, 40, 50, 40, 30, 25, 10, 5
length:     .word 10
sortedFlag: .word 0
lastUnsorted: .word 9
test:       .word 0

            .text
            .globlmain
main:
            la  $11, numbers
            lw  $12, length
            lw  $13, sortedFlag
            lw  $14, lastUnsorted
            lw  $15, test
            j while

end_main:

#####################################################################

while:
            li      $16, 1
            blt     $14, $16, end_while                     #program is completed
            li      $17, 0
            bne     $13, $17, end_while                     #program is completed
            addi    #13, 1                                  #make sortedFlag == 1
            j bubble_sort                                   #jump to the bubble sort

bubble_sort:
            bge     $15, $14, go_back                       #if test is greater than or equal to lastUnsorted, end
            ####stuff for swap

            # find address of first, then second and store each in t0 and t1
            # check the value at $t0 is greater than val at $t1; if so, call swap function
            addi    $15, $15, 1                             #add one to test after swap or no swap
            j       go_back                                 #jump out of sorting loop

go_back:
            addi    $14, $14, -1                            #subtract one from lastUnsorted
            j       while                                   #jump back to while loop to start again

swap:   
            move    $t2, $t0                                #swap with temporary registers??
            move    $t0, $t1
            move    $t1, $t2
            addi    $13, $13, -1                            #make sortedFlag == 0 IF a swap is completed

end_while:
            li  $vo, 10                                     #prog is done
            syscall

As you can see, I've left a piece of the middle blank, because I am not sure what to do to get the two elements and compare them. I found something online that said I could swap elements via move and temporary registers, but I don't see the connection between getting these elements and then swapping them. I realize the code is likely not optimal and there may be shortcuts, but I am very much a beginner on this.

Any advice would be appreciated! Thank you in advance.