Learn Hardcore Icelandic: Henni finnst minna gaman að vera einmana á kvöldin. - She finds it less fun to be lonely in the evenings.

So grammatically, Henni is like an indirect object in English (to her), but in Icelandic this dative phrase functions as what we’d call a “subject-like” experiencer.

What exactly does finnst mean here, and why that form?

Finnst is the 3rd person singular present of the verb finnast, which is related to finna (to find), but used in an impersonal way:

Mér finnst þetta gott.
I think this is good / This feels good to me.

So Henni finnst minna gaman … literally is:

To her, less fun is found … → She finds it less fun … / She enjoys it less …

You almost never see ég finnst; it’s always dative:

Mér finnst… (to me)
Þér finnst… (to you, sg.)
Okkur finnst… (to us)
Ykkur finnst… (to you, pl.)
Þeim / þeim / þeim finnst… (to them, masc./fem./neut.)

The verb always stays in 3rd person singular (finnst) when followed by a singular idea like gaman, even though the experiencer (mér, henni, þeim, etc.) changes.

What is gaman here? Is it an adjective like “fun” or something else?

Gaman is actually a neuter noun meaning something like fun, enjoyment, amusement.

In the common pattern:

Mér finnst gaman (að…)
Henni fannst ekki gaman.

it functions almost like an adjective in English, but grammatically it is a noun:

gaman (nom/acc sg. neuter)

So Henni finnst gaman að vera einmana á kvöldin. =
She finds it fun to be lonely in the evenings.

With minna in front, minna gaman = less fun (literally: less enjoyment).

Why is it minna gaman? What is minna doing here?

Minna here means less, forming a comparative phrase minna gaman = less fun.

A useful parallel:

mikið gaman = much fun / a lot of fun
meira gaman = more fun
lítið gaman = little fun
minna gaman = less fun

So minna is the comparative of lítið (little), working like an adverb/quantifier modifying gaman:

Henni finnst minna gaman…
She finds it less fun… / She enjoys it less…

You cannot put minna after gaman here; *gaman minna would be wrong in this sense. The normal pattern is [degree word] + gaman.

Could you rephrase the structure in a more English-like order to see what’s going on?

A rough “word-by-word logic” mapping is:

Henni – to her
finnst – seems / is found / she finds
minna gaman – less fun
að vera einmana – to be lonely
á kvöldin – in the evenings

So the Icelandic sentence corresponds roughly to:

To her, it is less fun to be lonely in the evenings.
→ more natural English: She finds being lonely in the evenings less fun (than before / than something else).

The Icelandic word order is quite natural for this construction:

[dative experiencer] + finnst + (meira/minna) gaman + að [verb phrase] + time phrase

Why do we need að in að vera einmana?

Að here is the infinitive marker, like to in English to be.

vera = to be (bare infinitive)
að vera = to be (infinitive with marker “to”)

After gaman in this construction, the action you enjoy (or don’t enjoy) is normally expressed with að + infinitive:

Mér finnst gaman að syngja. – I like singing.
Henni finnst gaman að lesa. – She likes reading.
Henni finnst minna gaman að vera einmana. – She likes being lonely less.

Dropping að here (*Henni finnst minna gaman vera einmana) would be ungrammatical.

Why is einmana used, and not something like einn or ein?

Einmana means lonely (emotionally). It’s different from einn/ein/eitt, which mostly means alone / by oneself (just physically alone).

Hún er ein. – She is alone (no one else is there; neutral).
Hún er einmana. – She is lonely (feels lonely).

A key point: einmana is (for practical purposes) indeclinable:

Hann er einmana. – He is lonely.
Hún er einmana. – She is lonely.
Þau eru einmana. – They are lonely.

It doesn’t change its ending for gender, number, or case. That’s why you don’t see einman / einmani / einmanað etc. here—einmana is the correct form for henni as well.

What does á kvöldin literally mean, and why that form of kvöld?

Á kvöldin literally is on the evenings but is best translated as in the evenings or at night (in the evenings) when talking about a habitual situation.

Grammatically:

kvöld – evening (neuter)
kvöldin – the evenings (nominative/accusative plural definite)

With time expressions, Icelandic often uses:

á + accusative to mean on / in (during) a time period.

Common patterns:

á daginn – in the daytime
á nóttunni – at night
á morgnana – in the mornings
á kvöldin – in the evenings

So á kvöldin expresses a repeated, general time frame: in the evenings (as a rule / usually), rather than a single specific evening.

Where is the “than” part? How would you say “than before / than in the daytime”?

The Icelandic sentence:

Henni finnst minna gaman að vera einmana á kvöldin.

often leaves the comparison implicit, just like English can:

She finds it less fun to be lonely in the evenings.
(less fun than what? – understood from context)

If you want to say it explicitly, you add en (than), just like English than:

Henni finnst minna gaman að vera einmana á kvöldin en áður.
She finds it less fun to be lonely in the evenings than before.
Henni finnst minna gaman að vera einmana á kvöldin en á daginn.
She finds it less fun to be lonely in the evenings than in the daytime.

Is there a more basic pattern I can learn and then just add minna?

Yes. Think of the core pattern as:

[dative pronoun] + finnst (gott / gaman) (að…)

For example:

Mér finnst gaman að læra íslensku. – I enjoy learning Icelandic.
Henni finnst gaman að horfa á sjónvarpið á kvöldin. – She enjoys watching TV in the evenings.

Then you can add meira (more) or minna (less) in front of gaman:

Mér finnst meira gaman að… – I find it more fun to…
Mér finnst minna gaman að… – I find it less fun to…

So your sentence fits this pattern:

Henni finnst minna gaman að vera einmana á kvöldin.
She finds it less fun to be lonely in the evenings.