How do you prevent glue from hardening too quickly, and how do you get glue into small spaces?

Glues set by many different mechanisms. Some set by heat, some with pressure, some by evaporation of solvents. Silicone and polyurethane set by reacting with moisture in the air. If your glue sets by evaporation, stay away from air currents and heat. You can also buy glues specially formulated to set quickly or slowly. Quick-setting glues are best for hard-to-clamp objects, slow glues are best for hard-to-assemble projects. To answer the second part of your question, to apply glue to small nooks and crannies you can either dab some glue on the end of a toothpick or shoot glue out of a plastic glue syringe found in most hardware and hobby stores.