Learn Hardcore Finnish: Otan puhtaan astian ja laitan sen pöydälle. - I take a clean dish and put it on the table.

Both otan (from ottaa, to take) and laitan (from laittaa, to put / to place) are 1st person singular (I) in the present tense.
Finnish present tense often covers what English might express as I take and put or I’m going to take and put depending on context.

Why does puhdas become puhtaan?

Puhtaan is the form of puhdas (clean) that matches the case/role of the noun it modifies. Here the phrase puhtaan astian is the object, and the object is in a form that looks like genitive/accusative singular.
Many adjectives change their ending to agree with the noun’s case:

base: puhdas
object form here: puhtaan (same ending pattern as the noun: astian)

What case is astian and why is it used here?

Astian is in the genitive-looking object form (often described as genitive/accusative singular, depending on the grammar explanation you follow). It’s used because the sentence describes taking a whole, specific item (a complete object), not just some of something.
So otan puhtaan astian means taking one (complete) clean dish/container.

How would it change if I meant “I take a clean dish (some amount / not the whole thing)”?

Then Finnish typically uses the partitive object:

Otan puhdasta astiaa is not natural because astia is a countable item (you don’t usually take “some dish”).
More realistic partitive examples are with mass nouns:
Otan puhdasta vettä = I take some clean water.

For countable nouns like astia, you normally take one whole item, so puhtaan astian is the expected choice.

What exactly does astia mean?

Astia is a general word for a dish / container / vessel, depending on context. It can refer to things like a plate, bowl, cup, or a container used for food or storage. In everyday speech it’s often understood as a dish in the broad sense.

Why is sen used—what does it refer to?

Sen means it (object form of se), and it refers back to astian (the dish/container).
So laitan sen pöydälle = I put it onto the table.

Why is it pöydälle and not pöydässä or pöydällä?

Pöydälle is the allative case and means onto the table (movement to the surface).
Compare:

pöydälle = onto the table (motion toward)
pöydällä (adessive) = on the table (location)
pöydässä (inessive) = in the table (inside it—usually not what you mean)

Is there a rule for choosing object forms like astian vs astiaa?

A common learner-friendly rule is:

Use the “total object” form (often -n) when the action is completed / bounded and the object is taken/handled as a whole: Otan astian.
Use the partitive (-a/-ä) when the action is ongoing, incomplete, habitual, or when you mean some of a mass/quantity: Otan vettä.

This sentence uses the total-object pattern because you take a whole dish and then place it.

Why does Finnish not need a separate word for “a” or “the” here?

Finnish has no articles like a/an/the. Whether astian means a dish or the dish is inferred from context. The grammar (like object case and pronoun sen) helps, but it won’t directly encode articles the way English does.

Could the word order be different?

Yes. Finnish word order is flexible, and changes often signal emphasis or information structure. Neutral here is:

Otan puhtaan astian ja laitan sen pöydälle.

But you could emphasize the location, for example:

Otan puhtaan astian ja laitan sen pöydälle (neutral)
…ja pöydälle minä sen laitan (emphatic/stylized: and onto the table I put it)
In normal conversation, the original order is the most natural.