Born into a modest family, he did several types of manual jobs during his youth (carpenter, mechanic, sugarcane worker, shoemaker), but quickly became interested in music, and especially in the guitar.

Puebla began by writing love songs, such as Quiero hablar contigo (I want to talk with you), Este amor de nosotros (This love of ours), Serenata cubana, Canción definitiva, Qué sé yo and Te vieron con él, which later became successes, and also Cuenta conmigo, Quién se lo iba a imaginar and Hay que decir adiós, popularised by the duo Clara and Mario.

Specifically, the Moncada assault of 1953 against the Batista Government impacted him and inspired Puebla to immortalize the date with the song, Para nosotros siempre es 26.

With the use of humor and irony, a collection of his poems criticizing the inefficiencies of the society and economy reflect what the common Cuban citizen felt during the revolutionary time period.

[4] His poems: Cine en Televisión, Cosa Ocurrida, La Espera and Otra nueva ilusión embody the thoughts and common sentiment of the Cuban community and give an understanding as to what they desired, change.

His most famous song, Hasta Siempre, Comandante, has been covered by dozens of artists from all over the world, notably in France, by Nathalie Cardone and Los Calchakis, although this last one is wrongly attributed to Buena Vista Social Club.