Laitan kirjan pois ja sammutan lampun.

In Finnish, the personal ending on the verb already tells you the subject, so laitan by itself means I put / I will put.

• laitan = I put
• laitat = you put
• laittaa = he/she puts

Because of that, the pronoun minä is often omitted unless you want emphasis or contrast.

• Laitan kirjan pois. = I’ll put the book away.
• Minä laitan kirjan pois. = I will put the book away. (more emphatic)

Grammatically, it is in the present tense. Finnish does not usually have a separate future tense like English does.

So Laitan kirjan pois ja sammutan lampun can mean:

• I put the book away and turn off the lamp
• I’m putting the book away and turning off the lamp
• I’ll put the book away and turn off the lamp

The exact time meaning depends on context.

They are objects, and in this sentence they are total objects: the actions affect the whole thing and are seen as completed.

• kirja → kirjan
• lamppu → lampun

Here:

• laitan kirjan pois = I put the whole book away
• sammutan lampun = I turn off the lamp completely

This -n form is very common for singular total objects in Finnish.

Because kirjan suggests a completed action affecting the whole object, while kirjaa would suggest a partial/incomplete/ongoing object in many contexts.

Compare:

• Laitan kirjan pois. = I put the book away. (finished action; the whole book)
• Luen kirjaa. = I am reading a book / the book. (ongoing action, so partial object is common)

With laittaa pois, the action is naturally complete, so kirjan is the expected form.

Pois usually means away or off, depending on context.

In laitan kirjan pois, it means away:

• put the book away

It often combines with verbs to show removal or moving something out of use or out of the way.

Examples:

• ottaa pois = take away / remove
• viedä pois = carry away
• laittaa pois = put away

Without pois, laitan kirjan feels incomplete to many learners because laittaa is a very general verb meaning put / place / set. It often needs some extra information:

• Laitan kirjan pöydälle. = I put the book on the table.
• Laitan kirjan laukkuun. = I put the book in the bag.
• Laitan kirjan pois. = I put the book away.

So pois tells us where/how the book is being put: not just somewhere, but away.

Sammutan is the 1st person singular form of sammuttaa, which means to turn off or to extinguish.

Its forms go like this:

• sammuttaa = to turn off
• sammutan = I turn off
• sammutat = you turn off
• sammuttaa = he/she turns off

It is used for things like lamps, lights, devices, fires, and so on.

Examples:

• Sammutan lampun. = I turn off the lamp.
• Sammuta televisio. = Turn off the television.
• Tuuli sammutti kynttilän. = The wind extinguished the candle.

The basic dictionary form is lamppu, but as the object here it becomes lampun.

This sentence uses a total object, so the singular object takes the -n form:

• lamppu = lamp
• lampun = the lamp (as a total object here)

Also note the stem change:

• lamppu → lampun

This is a normal Finnish pattern.

Yes, ja basically means and.

It joins the two actions:

• Laitan kirjan pois
• ja
• sammutan lampun

So the sentence means that the speaker does both actions.

Yes, Finnish word order is fairly flexible, although the most neutral order is the one given.

Neutral:

• Laitan kirjan pois ja sammutan lampun.

You can change the order for emphasis:

• Kirjan laitan pois ja sammutan lampun.
  Emphasizes the book.
• Lampun sammutan ja laitan kirjan pois.
  Emphasizes the lamp or changes the order of events.

So word order can shift, but the original sentence is the most natural plain statement.

Sometimes yes, depending on context. Lamppu literally means lamp, but in everyday use it can refer to a light source in a practical sense. So sammutan lampun is commonly understood as I turn off the lamp/light.

If you want to be more specifically about a light, Finnish also uses words like:

• valo = light
• Sammutan valon. = I turn off the light.

Both can be natural depending on the situation.

Yes: both verbs are in the same person and tense, and Finnish simply links them with ja.

• laitan = I put
• sammutan = I turn off

This is very straightforward and works much like English:

• I put the book away and turn off the lamp.

Finnish does not need to repeat the subject minä before the second verb unless there is a special reason for emphasis.

If you were telling one person to do it, you would use imperative forms:

• Laita kirja pois ja sammuta lamppu.

Notice the object forms may also change depending on style and structure, but this is the normal command version learners often meet first.

So:

• Laitan kirjan pois ja sammutan lampun. = I put / I’ll put the book away and turn off the lamp.
• Laita kirja pois ja sammuta lamppu. = Put the book away and turn off the lamp.