The most common case of when you use these (not counting the passive construction), is when you have a pronoun as the object of a verbal noun, as a verbal noun can't have a pronoun object.
So, instead, you change ag to do (in the standard), and add the possessive pronoun, with it affecting the VN in the normal way. Also remember that do + a = á and that do + ár = dár*
So you get:
- Táim do m'úsáid (I am using me).
- Táim do d'úsáid. (I am using you)
- Táim á úsáid. (I am using it(masc. object)/ I am using him)
- Táim á húsáid. (I am using it(fem. object)/I am using her)
- Táim dár n-úsáid. (I am using us)
- Táim bhur n-úsáid (I am using y'all)
- Táim á n-úsáid (I am using them)
As to a, you use it at times when you'd use the infinitive in English (so " to go", for example). However, it is only used if the infinitive has an object, in which case the object is fronted before the verbal noun, and you use a + leniton on the VN
- Is fearr liom ithe (I prefer to eat)
- Is fearr liom bia a ithe (I prefer to eat food)
- Is maith liom ceannach (I like to buy)
- Is maith liom bia a cheannach (I like to buy food)
The á means the thing being acted on is either an "it" or a "he". Stephan_87's example (Bhí an siopa á dhúnadh) literally means "The shop was in its closing", ie "The shop was being closed" since the most literal translation is really awkward in English.
Táim á úsaid literally means "I am at its using", which again needs to be modified a little to make sense. This is a different meaning from "I am being used."