Before a vowel, t' is usually written and pronounced as if appended to the following word.
In He can't make up his mind if he wants one or t'other (= He can't make up his mind if he wants one or the other) t'other is pronounced as if spelled "tother". Sometimes it is pronounced as a glottal stop.
Before a consonant, t' is pronounced as a glottal stop following the preceding word.
In I'm going down t' road to see me mam ( = I'm going down the road to see my mother), down t' is pronounced as down followed by a glottal stop.
t' is sometimes not pronounced at all, having no glottal stop.