The sharp leaves are chopped off to expose the heavy heart of the plant known as the piña.  This is where all the sugar collected over the life of the plant. The piñas can be cooked by a variety of methods.  This image shows the more traditional cooking method of brick ovens where the cooking continues for 3-5 days. 

The cooked piña are then shredded and crushed using a giant stone wheel called a tahona.   

The crushed piña fibers and liquid are left to ferment in a large vat.  The result is a kind of agave beer.  

That alcohol is then distilled twice to create a clear alcohol that can be bottled as tequila.

The tequila can be bottled as a blanco, or rested in wooden barrels to create aged tequilas. The ages are as follows. 

< 2 months in a barrel: blanco

2 - 12 months in a barrel: reposado

1 -3 years in a barrel: anejo

3+ years in a barrel: extra anejo

There is no objective age that is "better" than any other. Each person will have their own preference.  In general, the blanco will have the most agave flavor while the more aged varieties will turn up the volume on barrel flavors while turning down the agave flavor.

The traditional process described above is time consuming.  There is a more modern approach to tequila creation that uses a machine the size of a football field called a diffuser.  In some cases, there is no cooking at all. Instead, hydrochloric acid is used to convert starches into sugars.  To make up for the taste this creates, producers can add up to 1% of the volume in the bottle of flavor and color additives.  It can still be labeled as a 100% agave tequila even though 1% of the bottle is not tequila.  The only way to be sure you are purchasing a traditionally made tequila is by consulting this list of brands that have been subjected to third party inspection.  

https://tastetequila.com/2021/confirmed-additive-free-tequila-brands/