Käyn nopeasti suihkussa aamulla.

Yes, käyn is the 1st person singular of käydä, which often means to go, to visit, or to stop by.

But in expressions like käydä suihkussa, Finnish uses käydä idiomatically to mean doing something briefly or as part of a routine. So käyn suihkussa means I take a shower / I have a shower, not just I go in a literal movement sense.

Suihkussa is the inessive form of suihku, with the ending -ssa, which often means in.

So:

• suihku = shower
• suihkussa = in the shower

Finnish often expresses activities like this with a location form rather than a direct object. Compare:

• käyn suihkussa = I take a shower
• olen suihkussa = I am in the shower

So even though English uses a verb like shower, Finnish often uses a phrase that literally looks more like be/go in the shower.

They are related, but not the same.

• käyn suihkussa focuses on the whole activity: I take a shower
• menen suihkuun focuses on movement into the shower: I go into the shower / I’m going to take a shower

So in your sentence, käyn suihkussa is the natural choice if the point is the routine action itself.

Aamulla is a common time expression in Finnish. It is the adessive form of aamu.

• aamu = morning
• aamulla = in the morning

Finnish often uses the -lla/-llä ending with parts of the day:

• aamulla = in the morning
• päivällä = during the day
• illalla = in the evening
• yöllä = at night

So even though -lla/-llä often means something like on or at, with times of day it is just the normal way to say in the morning, in the evening, and so on.

Nopeasti means quickly.

It modifies the action, so käyn nopeasti suihkussa means that the shower happens quickly, or that you take a quick shower.

It comes from the adjective nopea = fast, quick.

• nopea = quick
• nopeasti = quickly

This is a very common way to make adverbs in Finnish.

Because käyn already tells you the subject is I.

Finnish verb endings usually make the subject clear, so personal pronouns are often left out unless they are needed for emphasis or contrast.

• Käyn nopeasti suihkussa aamulla. = I take a quick shower in the morning.
• Minä käyn nopeasti suihkussa aamulla. = same basic meaning, but minä adds emphasis, as in I do that.

So leaving out minä is completely normal.

By default, it most naturally sounds like a habit or routine:

• I take a quick shower in the morning
• I usually shower quickly in the morning

Finnish present tense often covers both simple present and habitual meanings. Context tells you whether it is a general routine or something happening right now / around now.

Without extra context, this sentence sounds like a normal morning habit.

This is a natural, neutral word order.

A rough breakdown is:

• Käyn = I take/go
• nopeasti = quickly
• suihkussa = in the shower
• aamulla = in the morning

Finnish word order is more flexible than English, but changing the order changes emphasis.

For example:

• Käyn nopeasti suihkussa aamulla. = neutral
• Aamulla käyn nopeasti suihkussa. = emphasizes in the morning
• Käyn suihkussa nopeasti aamulla. = possible, but less neutral in rhythm

So the original order is a very natural everyday sentence.

Käydä is the infinitive, and käyn is its 1st person singular present form.

Some present-tense forms are:

• käyn = I go / I take
• käyt = you go
• käy = he/she/it goes
• käymme = we go
• käytte = you all go
• käyvät = they go

So in this sentence, käyn simply means I do/go in the present tense.

It is a useful verb to learn because it appears in many common expressions, such as:

• käydä töissä = to go to work / be at work
• käydä kaupassa = to go to the store
• käydä saunassa = to take a sauna / go to the sauna
• käydä suihkussa = to take a shower