Alchemists aren't mentioned in the Spellcraft skill simply because the Alchemist wasn't around when the Core rules were written and it's never been updated.
The only key difference between a wizard learning and an alchemist is that alchemists do not need to decipher arcane writings before copying them.
Therefore, to copy a spell/formula to your formula book:
- Get a spell/scroll/formula book with a formula that an alchemist can use.
- If you were a Wizard you'd have to Understand the text DC 20 + the spell's level. Failure means trying again the next day. But alchemists don't need to do this.
- Study the formula for an hour.
- Understand the formula DC 15 + the formula/spell's level. Failure means try again in a week.
- Copy the formula into your own book. This takes 1 hour per formula level (0 = 1/2 hour) This takes 1 page/level and costs money to pay for materials (see below)
- If this was on a scroll then that scroll is used up and useless.
Note that you can take 10 on these checks if "your character is not in immediate danger or distracted".
Lvl Cost
0 5 gp
1 10 gp
2 40 gp
3 90 gp
4 160 gp
5 250 gp
6 360 gp
7 490 gp
8 640 gp
9 810 gp
Being a Wizard or an alchemist is expensive.
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.
Best Answer
Any alchemist can take the Promethean Disciple discovery at level 6. It gives you the Craft construct feat for free and the ability to use your ranks in Craft (alchemy) skill to meet the caster level requirements, and to use that skill to craft the golem regardless of the golem requirements.
The discovery also grants the alchemist the ability to use extracts as replacements for the required spells that have an extract equivalent. Spells that have no extract equivalent must be provided in another way, like having someone cast it for you, use magic items, or simply increase the DC of crafting the construct by 5.
Note that alchemists have Craft(Alchemy) as a class skill and access to the Crafter's fortune and Fox's Cunning extracts. By the time an alchemist can get this discovery, and assuming 6 ranks in alchemy and crafter's fortune, he or she already has a large modifier to Craft(Alchemy) rolls:
I previously included in the calculation above the competence bonus granted by the Alchemy class skill, but it only aplies to crafting alchemical items, so you cannot apply it when crafting constructs. Even with that restriction, a lone alchemist is quite capable to craft homunculi by himself easily (base DC 12) as soon as this discovery is available, and would be able to move to beefier constructs as he or she gains levels (golem recipe list here).
Alternatively, you can use the Promethean Alchemist archetype (thanks Shadowcraft for pointing out that). This archetype gives you access to that discovery as early as level 1, and gives you an Homunculus companion that levels with you (much like a ranger animal companion), but at the hefty price of losing access to both bombs and mutagens.
Lastly, I would like to challenge your assumption that alchemists cannot get item creation feats. Any alchemist can take Master Craftsman feat for the craft(alchemy) skill for a +2 bonus to that skill and the ability to qualify for Craft Wondrous Item feat. The last one opens the ability for crafting a lot of nice items, like the Homunculus clay, that allows to have a temporary, additional homunculus at the cost of expending an use of mutagen.
Both the discovery and the archetype come from the splat book Occult adventures, so it is 100% official Paizo material.