Let me first note that the term evolution applies to species rather than individual organisms (the OP says
do we have methods to drive an organism to evolve to suit some artificially induced circumstance?) Evolutionary changes happen over many generations, whereas the changes in a single organism during its lifetime are not really evolution - its genome remains pretty much the same.
Secondly, the obvious answer given by others - the artificial selection requires some qualification: while dogs, horses, cows and other domestic animals have evolved into separate species due to their cohabitation with humans, it is not always obvious that such evolution was a result of deliberate human efforts. Both in terms of its deliberateness, but also in terms of whether any such continuous effort lasted long enough for a new species to develop. We can however meaningfully speak of deliberately developing new breeds of plants and domestic animals.
Finally, there are multiple (sometimes ongoing) experiments of evolution in various closed ecosystems, experiments at deliberate development of microbial resistance to antibiotics (aka morbidostat) and so on. (I will add the references later.)