Intentionally preserved biological material in natural history collections represents a vast repository of biodiversity. Advances in laboratory and sequencing technologies have made these specimens increasingly accessible for genomic analyses, offering a window into the genetic past of species and often permitting access to information that can no longer be sampled in the wild. Due to their age, preparation and storage conditions, DNA retrieved from museum and herbarium specimens is often poor in yield, heavily fragmented and biochemically modified. This not only poses methodological challenges in recovering nucleotide sequences, but also makes such investigations susceptible to environmental and laboratory contamination. In this paper, we review the practical challenges associated with making the recovery of DNA sequence data from museum collections more routine. We first review key operational principles and issues to address, to guide the decision-making process and dialogue between researchers and curators about when and how to sample museum specimens for genomic analyses. We then outline the range of steps that can be taken to reduce the likelihood of contamination including laboratory set-ups, workflows and working practices. We finish by presenting a series of case studies, each focusing on protocol practicalities for the application of different mainstream methodologies to museum specimens including: (i) shotgun sequencing of insect mitogenomes, (ii) whole genome sequencing of insects, (iii) genome skimming to recover plant plastid genomes from herbarium specimens, (iv) target capture of multi-locus nuclear sequences from herbarium specimens, (v) RAD-sequencing of bird specimens and (vi) shotgun sequencing of ancient bovid bone samples.