"Madadh óg atá ann."
"Bó óg atá ann."
"Muc óg atá ann."
What would be the best translation for these?
I still get confused about "ann" and "atá ann".

Cheerio Texas

I'd say:

Madadh óg atá ann. "It's a young dog."
Bó óg atá ann. "It's a young cow."
Muc óg atá ann. "It's a young pig."

Await confirmation or correction ...

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Múinteoir Gaeilge - Irish Teacher
My "specialty" is Connemara Irish, particularly Cois Fhairrge dialect, but I can also speak Ulster and Munster Irish with native-level pronunciation.
Is fearr Gaeilge ḃriste ná Béarla cliste, cinnte, aċ i ḃfad níos fearr aríst í Gaeilge ḃinn ḃeo na nGaeltaċtaí.
Gaeilge Chonnacht (GC), go háraid Gaeilge Chois Fhairrge (GCF), Gaeilic Uladh (GU), Gaelainn na Mumhan (GM), agus Gaeilge an Chaighdeáin Oifigiúil (CO).

That's pretty much what I thought.
The sentences are from a children's book called Ag Fás.
A complete example of a page:
under a photo of a puppy it says
Seo coileán.
Madadh óg atá ann. (picture of a dog is next)

for the cow--
Seo gamhain.
Bó óg atá ann.

Thanks much for the quick assist, Breandán.

I get confused about ann knowing that in a sentence such as
Tá fear ann. "There is a man (there)." (at least per Ó Siadhail).

CheerioTexas

The two are not unrelated.

Madadh óg atá ann is actually short for Is madadh óg atá ann. "It is a young dog that is there."

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Múinteoir Gaeilge - Irish Teacher
My "specialty" is Connemara Irish, particularly Cois Fhairrge dialect, but I can also speak Ulster and Munster Irish with native-level pronunciation.
Is fearr Gaeilge ḃriste ná Béarla cliste, cinnte, aċ i ḃfad níos fearr aríst í Gaeilge ḃinn ḃeo na nGaeltaċtaí.
Gaeilge Chonnacht (GC), go háraid Gaeilge Chois Fhairrge (GCF), Gaeilic Uladh (GU), Gaelainn na Mumhan (GM), agus Gaeilge an Chaighdeáin Oifigiúil (CO).

I suppose that it's to point out or to define what a puppy is, but couldn't you also say Is madra é here?

Yes, you could. Is madra óg é is synonymous with Madra óg atá ann.

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Múinteoir Gaeilge - Irish Teacher
My "specialty" is Connemara Irish, particularly Cois Fhairrge dialect, but I can also speak Ulster and Munster Irish with native-level pronunciation.
Is fearr Gaeilge ḃriste ná Béarla cliste, cinnte, aċ i ḃfad níos fearr aríst í Gaeilge ḃinn ḃeo na nGaeltaċtaí.
Gaeilge Chonnacht (GC), go háraid Gaeilge Chois Fhairrge (GCF), Gaeilic Uladh (GU), Gaelainn na Mumhan (GM), agus Gaeilge an Chaighdeáin Oifigiúil (CO).

Is madadh óg atá ann. ("It is a young dog that is there.")
You use is here because what you're actually saying is
"It = young dog" (which used the copula) "that is (atá) there"?
Am I understanding that correctly?

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Múinteoir Gaeilge - Irish Teacher
My "specialty" is Connemara Irish, particularly Cois Fhairrge dialect, but I can also speak Ulster and Munster Irish with native-level pronunciation.
Is fearr Gaeilge ḃriste ná Béarla cliste, cinnte, aċ i ḃfad níos fearr aríst í Gaeilge ḃinn ḃeo na nGaeltaċtaí.
Gaeilge Chonnacht (GC), go háraid Gaeilge Chois Fhairrge (GCF), Gaeilic Uladh (GU), Gaelainn na Mumhan (GM), agus Gaeilge an Chaighdeáin Oifigiúil (CO).

BUT - if I wanted to say it's the dog - you have to say - Is é an madra é (and I seem to remember that in Munster you add on - ea é somewhere)

This ann is not ‘there’ generically speaking, but a more literal ‘in it (him)’.

In the same way as you can say tá sé ina XYZ, you can also turn this on its head and say XYZ atá ann. Had it been tá sí ina hXYZ or tá siad ina nXYZ, it would have been XYZ atá inti/iontu.

(There is a tendency to use ann instead of inti if the word is only grammatically feminine, but not obviously semantically so. So while many older Ulster speakers would still say leabaidh atá inti, most younger speakers would probably say leabaidh atá ann, because a bed is not semantically any particular gender)

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Not a native speaker.

Always wait for at least three people to agree on a translation, especially if it’s for something permanent.

My translations are usually GU (Ulster Irish), unless CO (Standard Orthography) is requested.