Stochastic processes play a vital role in the early stages of the evolution of drug-resistant malaria. We present a simple and flexible method for investigating these processes and understanding how they affect the emergence of drug-resistant malaria. Qualitatively different predictions can be made depending on the biological and epidemiological factors which prevail in the field. Intense intra-host competition between co-infecting clones, low numbers of genes required to encode resistance, and high drug usage all encourage the emergence of drug resistance. Drug-resistant forms present at the time drug application starts are less likely to survive than those which arise subsequently; survival of the former largely depends on how rapidly malaria population size stabilizes after drug application. In particular, whether resistance is more likely to emerge in areas of high or low transmission depends on malaria intra-host dynamics, the level of drug usage, the population regulation of malaria, and the number of genes required to encode resistance. These factors are discussed in relation to the practical implementation of drug control programmes.