Learn Hardcore Turkish: Onun gelmesine çok sevindim. - I was very happy about her coming.

gel-: come
-me: verbal noun (turns the verb into “coming”)
-si: 3rd person possessive (“his/her/its” coming)
-ne: dative case “to/for/about,” with a buffer n (because a case suffix comes after a 3rd-person possessive)

So gelmesine ≈ “to/about his/her coming.”

Why is it onun and not just o?

In Turkish, when a verb is turned into a noun (a nominalized clause), its subject appears in the genitive case and the nominalized verb takes a possessive suffix. That structure is called “genitive–possessive.” Hence:

onun gelmesi = “his/her coming” (genitive subject + possessed verbal noun) Using nominative o here would be ungrammatical.

Is onun required, or can I drop it?

You can drop it if the referent is clear from context:

Gelmesine çok sevindim. (I was very happy about his/her coming.) The 3rd person possessive -si already signals “his/her.” Keep onun for clarity or emphasis, especially if multiple third persons are in play.

Why does sevinmek use the dative (-e/-a) here?

Because the verb sevinmek (to be glad) typically takes the dative: you are glad “to/at/about” something.

Pattern: bir şeye sevinmek (to be happy about something) Hence: onun gelmesine sevinmek.

Where does the n in gelmesine come from?

It’s a buffer letter. When a case suffix follows a 3rd-person possessive (-sı/-si/-su/-sü), Turkish inserts n for smooth pronunciation:

gelme-si-ne, ev-i-ne, okul-u-na.

How is this different from Onun geldiğine/geleceğine/gelişine çok sevindim?

Onun gelmesine: focuses on the event “his/her coming” in general as a noun; often used when the coming is planned/expected or spoken of as an occasion.
Onun geldiğine: uses the -DIK nominalization; it presents the coming as a fact (“that he/she came”)—good when it actually happened.
Onun geleceğine: future-oriented (“that he/she will come/would come”).
Onun gelişine: uses the lexical noun geliş (“arrival”); slightly more concrete or stylistic, but very natural.

All four are correct; choose based on whether you want general event, factual past, explicit future, or the noun “arrival.”

So does gelmesine mean the person already came, is coming, or will come?

By itself it doesn’t fix the time; it treats “coming” as an event. In practice:

If you’re reacting to a plan/invitation, it often implies a future or expected coming.
If you want to be explicit about a completed action, use geldiğine.
If you want to be explicit about a future action, use geleceğine.

Can I say O gelmesine çok sevindim?

No. The subject of a nominalized verb must be in genitive: onun. So the correct form is Onun gelmesine çok sevindim (or drop the pronoun if clear: Gelmesine çok sevindim).

Can I move the words around? Where does çok go?

Word order is flexible for emphasis. Common options:

Onun gelmesine çok sevindim. (neutral)
Çok sevindim onun gelmesine. (emphasis on how glad you were) Keep çok near sevindim. Avoid Onun çok gelmesine sevindim (that suggests “his coming a lot,” which is odd).

What’s the difference between sevindim and sevdim? They look similar.

sevinmek → sevindim: “I was glad/I became happy.”
sevmek → sevdim: “I loved/I liked.” They are different verbs. Don’t say Onun gelmesini sevdim if you mean “I was glad that he came”; that means “I liked his coming.”

Is there a causative alternative?

Yes: Onun gelmesi beni çok sevindirdi.

sevinmek (to be glad) is intransitive.
sevindirmek (to make someone glad) is causative/transitive. This shifts the focus to “His coming made me happy.”

How do I change the sentence for different people?

“I’m glad that you (singular) came/are coming”: Senin gelmene çok sevindim.
“I’m glad that you (plural/formal) came/are coming”: Sizin gelmenize çok sevindim.
“I’m glad that they came/are coming”: Onların gelmelerine çok sevindim. You can also use names: Ahmet’in gelmesine çok sevindim.

How do I make it negative or ask a question?

Negative: Onun gelmesine hiç sevinmedim. (I wasn’t happy about his/her coming at all.)
Yes/no question: Onun gelmesine sevindin mi?
Habitual: Onun gelmesine sevinirim. (I’m/ I would be glad about his coming.)

Is çok necessary? Any alternatives?

No, it’s optional. Sevindim already means “I was glad.”

Softer: epey sevindim, pek sevindim (register varies).
Stronger emphasis: çok ama çok sevindim, aşırı sevindim (colloquial).

Could I use mutlu olmak or memnun olmak instead of sevinmek?

Onun gelmesine çok mutlu oldum is acceptable and means roughly the same, though sevindim is the most idiomatic reaction to good news.
memnun olmak selects the ablative: Onun gelmesinden çok memnun oldum. (Note the case change: memnun + -den.)