[RPG] For Pathfinder, how to go about creating mutagens and extracts as an alchemist

It seems to me that your question is two fold. I may be wrong but you seem to be looking not only for a technical point of view but also from a role-play point of you.

The technical aspect is quite easy to answer:

You will need two items to produce your concoctions(extracts, mutagens and bombs):

Kit, Alchemy Crafting

Price 25 gp; Weight 5 lbs.

An alchemist with an alchemy crafting kit is assumed to have all the material components needed for his extracts, mutagens, and bombs, except for those components that have a specific cost. An alchemy crafting kit provides no bonuses on Craft (alchemy) checks. (This item was previously called an “alchemist's kit”, and was renamed to avoid confusion with the set of adventuring gear called an “alchemist's kit.”)

The second item is your

Formula Book

An alchemist may know any number of formulae. He stores his formulae in a special tome called a formula book. He must refer to this book whenever he prepares an extract but not when he consumes it. An alchemist begins play with two 1st-level formulae of his choice, plus a number of additional forumlae equal to his Intelligence modifier. At each new alchemist level, he gains one new formula of any level that he can create. An alchemist can also add formulae to his book just like a wizard adds spells to his spellbook, using the same costs, pages, and time requirements. An alchemist can study a wizard's spellbook to learn any formula that is equivalent to a spell the spellbook contains. A wizard, however, cannot learn spells from a formula book. An alchemist does not need to decipher arcane writings before copying them.

Extract's preparation How to make an extract. Most of the text around extract can be reduced to the funny (or not) "spell in a bottle".

In many ways, they behave like spells in potion form [...] An extract, once created, remains potent for 1 day before becoming inert, so an alchemist must re-prepare his extracts every day. Mixing an extract takes 1 minute of work—most alchemists prepare many extracts at the start of the day or just before going on an adventure, but it's not uncommon for an alchemist to keep some (or even all) of his daily extract slots open so that he can prepare extracts in the field as needed.

Alchemist extract are like spell really but with a kick they don't take as long to prepare, unless you have more than 60 extracts and at this point well... breaking action economy should not be too hard. The downside is that you need to redo it every day so no storing for long winter nights!

Mutagen's preparation

Now comes the preparation aspect on how to make Mutagens. As far as I can tell, the usual in D&d is to be quite abstract and left to the imagination of the player the details. Most of the time for spell caster you have to go into splat book and descriptions to get a "look and feel" and not only the "use a standard action".

Mutagen (Su)

At 1st level, an alchemist discovers how to create a mutagen that he can imbibe in order to heighten his physical prowess at the cost of his personality. It takes 1 hour to brew a dose of mutagen, and once brewed, it remains potent until used. An alchemist can only maintain one dose of mutagen at a time—if he brews a second dose, any existing mutagen becomes inert. As with an extract or bomb, a mutagen that is not in an alchemist's possession becomes inert until an alchemist picks it up again.

Emphasize mine... A mutagen is brewed, so it is likely to be prepared like a potion or extract but being far more potent it takes a whole hour to make one dose and the alchemist aura can only "power up" one at a time.

From the Alchemy crafting Kit, we know that you have all you need is in it.

So you now have the physical elements and you know that it takes you an hour to brew it.

I hope this will be sufficient for you to feel comfortable using your mutagen.