Cum pater tandem domum rediit, puella non statim locuta est, sed demum osculum ei dedit.

Here cum means when:

Cum pater tandem domum rediit = When the father finally returned home

This is a very common use of cum with the indicative, simply giving the time when something happened.

It does not mean with here.
Latin cum can mean both with and when, but the context makes the meaning clear.

Because this is a straightforward temporal clause: when the father returned home.

Latin often uses:

• cum + indicative for a simple factual time clause
• cum + subjunctive for a more circumstantial or background idea, especially in more literary styles

So here, cum ... rediit just states the event plainly: the father came home, and then the next thing happened.

Domum is a special idiomatic accusative meaning homeward / to home.

So:

• domum = home
• domi = at home
• domo = from home

Latin very often uses no preposition with words like domus and with names of towns and small islands when showing motion toward a place.

So domum rediit means he returned home, not he returned the house.

Rediit is the 3rd person singular perfect active indicative of redeo, redire, redii/redivi, reditum = to go back, return.

So rediit means:

• he returned
• she returned
• it returned

Here, because the subject is pater, it means he returned.

This is because loquor, loqui, locutus sum is a deponent verb.

A deponent verb:

• has passive-looking forms
• but an active meaning

So:

• locuta est looks like was spoken
• but actually means she spoke or she has spoken

Here it is the perfect tense of loquor.

Also, locuta is feminine singular because it agrees with puella. If the subject were masculine, it would be locutus est.

These two adverbs create a contrast:

• statim = immediately, at once
• demum = only then, at last, not until then

So the sentence means something like:

• the girl did not speak immediately, but only then gave him a kiss
• or more naturally, the girl did not speak right away, but instead finally gave him a kiss

The contrast is important:

• non statim = not right away
• sed demum = but only after a delay / but at last

They are similar, but not identical.

• tandem often means at last, finally, sometimes with a sense of waiting or relief
• demum often means only then, not until then, at last

So:

• pater tandem domum rediit = the father finally came home
• sed demum osculum ei dedit = but only then / at last she gave him a kiss

In other words:

• tandem describes the father’s delayed return
• demum describes the girl’s delayed response

Ei means to him and is in the dative singular.

The verb do, dare, dedi, datum = to give often takes:

• a direct object in the accusative: the thing given
• an indirect object in the dative: the person to whom it is given

So here:

• osculum = a kiss (direct object)
• ei = to him (indirect object)
• dedit = she gave

So literally:

she gave a kiss to him

Natural English:

she gave him a kiss

Because he is not the direct object of gave.

In she gave him a kiss:

• a kiss is what she gave
• him is the person receiving it

So Latin uses:

• osculum in the accusative
• ei in the dative

If Latin used eum, that would make him a direct object, which would not fit the grammar of dedit here.

All three are in the perfect tense.

In this context, the Latin perfect usually corresponds to the English simple past:

• rediit = returned
• locuta est = spoke
• dedit = gave

The Latin perfect can sometimes also be translated with English has ..., but in a narrative sentence like this, the simple past is usually best.

Latin word order is much more flexible than English word order because Latin endings show grammatical function.

For example:

• pater is clearly the subject
• domum shows motion toward home
• osculum is the direct object
• ei is the indirect object

So Latin can arrange words for emphasis and rhythm.

In this sentence, the order helps the flow of the story:

• first the background event: When the father finally came home
• then the girl's reaction: the girl did not speak immediately
• then the surprising action: but instead gave him a kiss

English depends much more on word order for grammar, while Latin often uses it for style and emphasis.

Classical Latin has no articles equivalent to English the and a/an.

So:

• pater can mean father or the father
• puella can mean girl or the girl
• osculum can mean a kiss or the kiss

The context tells you which is most natural in translation. In this sentence, English idiom usually prefers:

• the father
• the girl
• a kiss

Not by itself in the same way English said works.

Loquor usually means speak, talk, or say in a general sense, but it does not normally introduce direct speech as neatly as English say. If Latin wanted to report exact words, it might use other constructions or verbs depending on context.

So here puella non statim locuta est is best understood as:

• the girl did not speak immediately
• the girl did not speak right away

That is more natural than the girl did not say immediately.