Η μικρή χαμογελάει όταν βλέπει το ουράνιο τόξο.

Because in Greek, an adjective can be used like a noun when the context makes the meaning clear.

• μικρή is the feminine singular form of μικρός = small / little
• With the article η, it becomes η μικρή = the little one or the little girl

In natural English, we usually do not say the little, so we add a noun such as girl if the context suggests it.

Greek adjectives must agree with the noun they describe, or with the implied noun if the adjective is being used by itself.

Here the phrase is feminine singular:

• η = feminine singular the
• μικρή = feminine singular form of small/little

So the sentence is talking about a female person: the little girl / the little one.

Compare:

• ο μικρός = the little boy / the little one (masculine)
• η μικρή = the little girl / the little one (feminine)
• το μικρό = the little thing / little one (neuter)

χαμογελάει is the 3rd person singular present tense of χαμογελάω / χαμογελώ, meaning to smile.

So:

• χαμογελάω / χαμογελώ = I smile
• χαμογελάει = he/she/it smiles

In this sentence, it means she smiles.

You may also see χαμογελά instead of χαμογελάει. Both are used in Modern Greek.

Because Greek often leaves out subject pronouns when the verb ending already shows who the subject is. This is very common.

So instead of saying:

• Η μικρή χαμογελάει όταν αυτή βλέπει...

Greek normally just says:

• Η μικρή χαμογελάει όταν βλέπει...

The subject she is understood from the context and from the verb form.

όταν means when.

It introduces a time clause:

• όταν βλέπει το ουράνιο τόξο = when she sees the rainbow

In this sentence, it connects the two actions:

• she smiles
• when she sees the rainbow

So όταν works much like English when.

βλέπει is the 3rd person singular present tense of βλέπω = to see.

It is present because the whole sentence describes a general or repeated situation:

• The little girl smiles when she sees the rainbow

That is, whenever that situation happens, she smiles.

So the present tense in both verbs is very natural here.

It is the direct object of βλέπει, so it is in the accusative case.

She sees what?

• το ουράνιο τόξο

That makes it the object.

A useful thing to know is that many neuter singular nouns look the same in the nominative and accusative, so:

• nominative: το ουράνιο τόξο
• accusative: το ουράνιο τόξο

The form does not change here, but its role in the sentence does.

το ουράνιο τόξο is the normal Greek expression for rainbow.

Literally, it is something like:

• ουράνιο = heavenly / celestial / of the sky
• τόξο = bow

So the literal image is the heavenly bow or sky bow.

This is a fixed expression, so learners should treat το ουράνιο τόξο as the standard way to say rainbow.

Because ουράνιο is an adjective agreeing with τόξο, which is neuter singular.

Greek adjectives must agree in:

• gender
• number
• case

Since τόξο is neuter singular, the adjective also appears in the neuter singular form:

• ουράνιος = masculine
• ουράνια = feminine
• ουράνιο = neuter

So:

• το ουράνιο τόξο

is grammatically matched.

Yes. Greek word order is more flexible than English word order, because endings and articles show the grammatical relationships.

The sentence here has a very neutral order:

• Η μικρή χαμογελάει όταν βλέπει το ουράνιο τόξο.

But Greek can move parts around for emphasis, for example:

• Όταν βλέπει το ουράνιο τόξο, η μικρή χαμογελάει.

This still means the same thing, but it puts more focus on the when-clause first.

A rough pronunciation is:

ee mee-KREE ha-mo-ge-LA-ee O-tan VLE-pee to oo-RA-nio TO-kso

A few helpful notes:

• η sounds like ee
• χ sounds like a throaty h/k sound, not like English ch
• γ before ε or ι sounds like a soft sound, somewhat like the y sound blended with a fricative
• βλέπει is stressed on the first syllable: VLE-pee
• τόξο is stressed on TO

The accent marks show which syllable is stressed.

For example:

• μικρή → stress on the last syllable
• χαμογελάει → stress on λά
• βλέπει → stress on βλέ
• ουράνιο → stress on ρά
• τόξο → stress on τό

Stress matters in Greek pronunciation, so accent marks are important and should be learned as part of the word.

Not necessarily. Greek present tense can cover both a simple present and, depending on context, something similar to an English progressive.

Here, the most natural English translation is usually:

• The little girl smiles when she sees the rainbow.

But depending on context, Greek present forms can sometimes also be understood in a more ongoing sense.

So χαμογελάει here is best understood simply as smiles.