A nesting site is prepared in advance using a suitable container. A 5 gallon aquarium with a sliding lid will do. The wasps will need a source of cellulose to make paper for the nest, food for the larvae and food for the adults. Wasps are predatory. Caterpillars are perhaps the best source of food. Small crickets can do. The adults feed on nectar. Sugar water (10 percent sucrose) works. However, the dilute solution will mold and must be frequently replaced. Once the materials are assembled, the container is ready to house a colony.
Paper wasp colonies can be relatively easily established by collecting a foundress queen. The best time to do this is early summer when nests are small and defenders are few. Like most insects, wasps require a minimum temperature for their wings to function. Chilling them can render them unable to fly. This allows the nest to be manipulated without interference from the wasp. The nest can be attached to the top of the container. When all is ready, the foundress is released into the container. She will find the nest and the colony is ready to go.
Wasps are capable of learning. They can learn to distinguish between threats and non-threats. In a managed colony, wasps may associate human fingers with availability of food rather than a threat. Pet wasps will feed on sugar solutions from a human finger without stinging. Maculifrons provides the video (below). It is possible to keep wasp colonies without being stung, however, it is always a possibility. People who are highly allergic to wasp stings should not try this at home.