When I would teach this to my preservice teachers, I would get out the Unifix cubes and make them build the models for the numbers. (You might be able to find base-n blocks for some smaller values of n, but maybe not and they might be expensive.) If the number was 221 (base 3) = ___ (base 5), then they would use the cubes to make 2 3x3 squares, 2 3x1 rods and 1 extra piece. Then they could take them apart and try to make as many 5x5 squares as possible, then 5x1 rods and then count the left over pieces.

The nice thing about this is that the reinforces the notion of place value and from this, many students begin to develop their own informal (and eventually formal) notions and algorithms for non-decimal bases. For example, if they have more than 5 of something, they should be able to see how it would form the next largest piece and why the available numerals have changed. (It also lends itself very naturally to the same processes with multiplication and division, but that's more than you are asking.)

If you are interested in more details, I can email you some stuff about this, including specifics on some of the models and some of the problems that I've used in the past. I know that a nice, quick and snappy algorithm for just plugging and chugging might be what you are looking for, but I found that when we did that and they didn't have any understanding, mistakes were everywhere. Let me know if you are interested in any more of this at smit3397umn.edu.