We describe the steps involved in performing searches for sources of transient radio emission such as Rotating Radio Transients (RRATs), and present 10 new transient radio sources discovered in a re-analysis of the Parkes Multi-beam Pulsar Survey. Followup observations of each new source as well as one previously known source are also presented. The new sources suggest that the population of transient radio-emitting neutron stars, and hence the neutron star population in general, may be even larger than initially predicted. We highlight the importance of radio frequency interference excision for single-pulse searches. Also, we discuss some interesting properties of individual sources and consider the difficulties involved in precisely defining a RRAT and determining where they fit in with the other known classes of neutron stars.