Aventarse literally means to throw oneself with force. The Diccionario del español de México gives it a popular sense: “Atreverse o decidirse a hacer alguna cosa” (to dare or to decide to do something).
Its example: “¿Qué dices si nos aventamos y nos casamos de una buena vez?” (What do you say, shall we dare and get married once and for all?) Entrarle a algo means to take part in an activity, as in “Hay que entrarle a los tacos.”
Haciendo y deshaciendo se va aprendiendo, “by doing and undoing, one learns.” A lesson of the SEP, Mexico’s education ministry, for the first year of secondary school carries the saying as its title. It says: “es necesario crear experiencias que te hagan aprender de los errores” (it is necessary to create experiences that make one learn from mistakes).