There might be more efficient ways, but here's one way in 6 lines:
sll $t2,$t3,2 # t2 = i * sizeof(int)
addu $t2,$t2,$s1 # t2 = &B[i]
lw $t0,0($t2) # t0 = B[i]
sll $t0,$t0,2 # t0 *= sizeof(int)
addu $s0,$s0,$t0 # s0 = &A[B[i]]
lw $t0,0($s0) # t0 = A[B[i]]
Read a MIPS instruction set reference to get more information about what individual instructions do.