Käytyäni jäteasemalla huomasin, että sinne voi viedä myös vanhoja puhelimia.

It means after I had been to or after visiting.

This is a compact Finnish way to show that one action happened before the main action. Here:

• Käytyäni jäteasemalla = After I had been to the waste station
• huomasin = I noticed

A fuller version would be:

• Kun olin käynyt jäteasemalla, huomasin...

So the meaning is basically the same, but käytyäni is more compressed.

The ending -ni shows that the subject is I.

So käytyäni tells you that I am the one who had gone there. That matches the main verb huomasin (I noticed).

This kind of structure normally refers to the same subject as the main clause. In other words:

• I visited the waste station
• I noticed something

Both are correct, but they differ in style.

• Käytyäni jäteasemalla huomasin... is more compact and a bit more written/formal.
• Kun olin käynyt jäteasemalla, huomasin... is more explicit and often feels more conversational.

For a learner, the kun olin käynyt version is usually easier to understand at first, but the shorter käytyäni pattern is very common in written Finnish.

Because the noun asema usually takes the adessive ending -lla/-llä when you mean at the station.

So:

• jäteasema = waste station
• jäteasemalla = at the waste station

Finnish location forms are often partly idiomatic, so you usually learn them together with the noun or expression. Here käydä jäteasemalla is the natural phrase.

Here käydä means something like go to, visit, or stop by.

It does not mean walk in this sentence. So:

• käydä jäteasemalla = go to / visit the waste station
• compare: käydä kaupassa = go to the store
• käydä lääkärissä/lääkärillä = go to the doctor

It often has the sense of going somewhere and then coming back, or just making a visit.

Because että introduces the clause that tells what was noticed.

• huomasin = I noticed
• että sinne voi viedä... = that you can take there...

So huomasin, että... means I noticed that...

In English, that is sometimes omitted, but in Finnish että is very normal in this structure.

Because viedä involves movement to a place.

• sinne = to there
• siellä = there / at there

Since the phones are being taken to the waste station, sinne is the correct choice:

• sinne voi viedä = you can take/bring there

If you said siellä, it would suggest location rather than movement.

Finnish often uses the 3rd person singular verb in a generic way.

So sinne voi viedä myös vanhoja puhelimia means something like:

• you can also take old phones there
• one can also bring old phones there
• people can also take old phones there

It is a general statement, not about one specific person.

Because vanhoja puhelimia is in the plural partitive, which is natural here for an indefinite, non-specific object.

The sentence is talking about old phones in general, not a specific known set of phones.

So:

• vanhoja puhelimia = old phones / some old phones / old phones in general
• vanhat puhelimet = the old phones or those specific old phones

Also notice that both words match:

• vanhoja = partitive plural of vanha
• puhelimia = partitive plural of puhelin

Here myös most naturally means also old phones.

So the idea is probably that the waste station accepts other things, and the speaker realized that old phones are accepted too.

Word order affects emphasis in Finnish. In this sentence:

• sinne voi viedä myös vanhoja puhelimia

the focus is on vanhoja puhelimia being an additional thing you can bring.

Yes, but the first part is a little more compact than everyday speech often is.

A spoken-style version might be:

• Kun olin käynyt jäteasemalla, huomasin, että sinne voi viedä myös vanhoja puhelimia.

The original sentence is perfectly natural, especially in writing or careful speech. So it is not strange at all, just slightly more condensed.