I'm still in the very-early stages of learning, and I'm working through pronunciation. I'm currently using Teach Yourself Irish (Diarmuid Ó Sé) and various Wikipedia pages.

The spelling seems a bit ambiguous at times.

For example, "máthair".

The book and wikis say that the combination of "ai" would be pronounced /a/. On the other hand, the "a" following "th" could simply be a broad indicator, meaning the "pair" would be /ɪ/.

I'm admittedly a bit more accustomed to languages like Spanish or Polish, where the connection between pronunciation and spelling is more clear. Am I looking at this the wrong way?

No, Irish is not phonetic in that sense.
ai in an unstressed syllable is pronounced /i/, usually, but you could type the words into the pronunciation database at https://www.teanglann.ie/en/fuaim/ to check. You will have to pick a dialect.

Awesome. I feel substantially less dumb, now. This book's pronunciation guide is awful.

That book is not recommended, as it teaches a made-up "Standard Irish", devised by a committee in Dublin and not used by native speakers. As for pronunciation, Connacht is the majority dialect nowadays, and if you use the link I gave you and select Connacht pronunciation, you will have the pronunciation used by most native speakers. There are better books for Connacht Irish, including Learning Irish by Mícheál Ó Siadhail.

Aaah, that's disappointing, but thank you for pointing that out. You think the Connacht dialect would be a better fit?

Well, people tend to choose dialects based on their location (eg if you're in Munster, choose Munster) or their ancestry (if they have Ulster ancestors, they might chose Ulster). The Connacht dialect is better represented in the media, it seems (let's see if anyone says that's not true). Standardised Irish could be described as a mix of Connacht and Munster with only occasional nods to Ulster. I think the Standard is more Connacht, though. Basically, it's up to you.

Spelling and pronunciation differs a lot in Irish, esp. in the dialects.
There's a kind of School Irish using a more straitforward "standardized" pronunciation with a closer connection to (standardized) spelling.

In case of máthair:
Vowels in unstressed syllables are mostly always reduced to /ə/ (the first a in "again"), in slender environments tending to /​ɪ/ (the i in "with"), i.e. a bit more fronted and more closed than the middle /ə/.
Phonemically, it is the "same".
So the -ai- is already solved.

m, th, r are easy: broad /m/, /h/, slender /r´/
But in Cois Fharraige, a Connacht region, th /h/ between vowels is silent. And so the following ai /ə/ is silent, too.
á is /ɑ:/ in most dialect. Except for Ulster where it is often /​æ:/. But in máthair it is /ɑ:/, too.

So:
máthair /mɑ:hər´///mɑ:hɪr´/ everywhwere,
except in Cois Fh. with silent /h/: /mɑ:r´/.

Labhrás, can you recommend a dialect for the OP? Would you advise a learner, faute de mieux, to learn the Connacht pronunciation?

Another thing, Zzig, is that, while not phonetic as such, there is an underlying logic to the Irish spelling system, albeit varying from dialect to dialect, and over time you will more or less be able to work out the pronunciation from the spelling. Not in every single case, but mostly. Just as in English, in fact.

Oh, I believe that. This is more of a problem because I'm still very new to Irish.