I'm assuming you mean converting whole numbers, integers.  
Converting fractions is different.

For octal, the algorithm is this, starting with the first digit

Multiply by 8
Add next digit
Multiply by 8
Add next digit
.....

In hex, just use 16 instead of 8, and remember that A=10, B=11, etc.

until you run out of digits.

Suppose you have the octal number 

647210538

Start with first digit 6

               6
      6*8+4 =  52
     52*8+7 =  423
    423*8+2 =  3386
   3386*8+1 =  27089
  27089*8+0 =  216712
 216712*8+5 =  1733701  
1733701*8+3 = 13869611

647210538 = 1386961110

Suppose we have the hex number:

D59A52C16

You might want to write it this way first:

(13)59(10)52(12)

Start with D which is 13

                 13
      13*16+5  = 213
     213*16+9  = 3417
    3417*16+10 = 54682
   54682*16+5  = 874917
  874917*16+2  = 13998674
13998674*16+12 = 223978796

So D59A52C16 = 22397879610 
 
It's very easy with a TI graphing calculator, because when
you press *16+ after a calculation you don't have to reenter
the last number, it just automatically uses it as Ans and you
see Ans*16+.  So it's very fast on a TI.

Edwin