Colgarse means to use more time that is allotted, to exceed a time limit. Colgado can be used in reference to a person who often se cuelga and also to a place that is far, far away (i.e. getting there takes a long time). Le cuelga (literally, 'it hangs from it') means 'it is still going to take a while.'
Descolgarse means to go from one's current location to another, usually to meet other people and hang out. Just like a monkey would descend from a tree, a buddy unhangs from his place to meet friends.
Faustino: Descuélgate al reven. Va a estar de huevos. Van a caer un titipuchal de pieles.
Melquiades: Pus la neta sí me late, pero tu cantón está súper colgado.
Faustino: Come to the party. It'll be a lot of fun. There will be bueatiful women aplenty.
Melquiades: I truly like the idea, but your place is really far away.
Melamina: Este maestro siempre se cuelga con sus clases.
Ponderosa: Y todavía le cuelga para que concluya este semestre.
Melamina: This professor always stretches his lectures well pass the limit.
Ponderosa: And it's gonna be a while before the semester is over.
Note: Colgado is also used in expressions such as no me vayas delar colgado or me dejaste colgado hijo de la chingada. In this case, colgado is a reference to the metaphor colgado de la brocha, i.e. hanging from a paintbrush. Hence when somebody abandons you, it's perfectly fine to say that metaphorically such person removed the ladder you were on and left you hanging from the paintbrush.