"Téann sé go dtí an príosún."
Translation:He goes to the prison.
So to clarify, does this have the meaning of someone going to a prison (e.g. to work or to visit) but not going to prison (i.e. incarcerated)?
It literally means that he goes to the prison. It's not specific as to why he is going there.
Why is go dtí instead of go there? Is it because of the an or can't go be used in the meaning of towards?
It's because of the an.
If the destination doesn't have a definite article, you normally just use go (go dtí is sometimes used when the an isn't there), but if the an is there, you must use go dtí.
Note that it's not just used with physical destinations - you would also say go hAoine or go dtí an Aoine.
If he had gone to prison in the sense 'to stay, as a prisoner' would it then be 'téann sé chun príosún' ?
No, "prison" generally takes the definite article in Irish. The examples given in the NEID include:
"she spent three years in prison" - chaith sí trí bliana sa phríosún
"he was released from prison" - scaoileadh amach as an bpríosún é
"to break out of prison" - éalú as an bpríosún, briseadh amach as an bpríosún
"to send sb to prison" - duine a chur sa phríosún
But it's not a hard and fast rule - the entry for "sent" includes this entry, with two versions, one without the definite article, the other with:
"he was sent to prison" - cuireadh i bpríosún é, cuireadh sa phríosún é
chun is used in some examples of "to prison":
"she was committed to prison" - cuireadh i bpríosún í, daoradh chun príosúin í
"they were marched away to prison" -tugadh ar shiúl chun an phríosúin iad
"the judge was queasy about sending an old man to prison" - bhí drogall ar an mbreitheamh seanfhear a chur chun an phríosúin
"he was sent to prison - can't say I'm sorry" - cuireadh chun an phríosúin é - ní cúis aiféala ar bith dom é
But other examples translate "sent to prison" as "put in prison" - cuireadh sa phríosún:
"to cast sb into prison" - duine a chaitheamh isteach i bpríosún
"they were flung into prison" - caitheadh i bpríosún iad, sacadh isteach sa phríosún iad
"he was sent to prison for the rest of his natural life" - cuireadh i bpríosún é don chuid eile dá shaol
"the judge ordered that she should be sent to prison" - d'ordaigh an breitheamh go gcuirfí sa phríosún í, thug an breitheamh ordú í a chur sa phríosún
"some pickets were sent to prison" - cuireadh cuid den lucht picéid sa phríosún
The bottom line is that, just as in English, there are a couple of different idioms that overlap, and that context and the writers own preferences will dictate which one is used.
Br Eng seems to offer a different structure here than either Am Eng or Ir.
I go to prison (I am incarcerated) I go to the prison (I go to a specific prison for an unspecified reason) I go to hospital (I am admitted for treatment to an unspecified hospital) I go to the hospital (I go to a specific hospital for an unspecified reason)
The distinction applies to all varies of English (except for hospital), but as Knocksedan clarifies, not in Irish. I go to school/I go to the school etc. His examples are excellent