As you should know, cha(n) is an Ulster variant of ní, i.e. “not”. It is also Scottish Gaelic. However, it is not entirely correct to say that you can or should use it everywhere instead of ní. Not that it would be quite wrong either.
I think there are people in the Six Counties who want to do their utmost to recreate the dialect once spoken there. While I am sympathetic to such attempts, I preferred myself, back when I still aspired to pure Ulster Irish, to get a thorough grounding in the native literature and folklore of the whole province – and only after that did I start to incorporate quintessentially East Ulster expressions. You see, the problem with zooming in on a very narrow dialect zone is that all the written material available in that dialect can be the language of terminal speakers, i.e. speakers who hadn’t used it as a community language for a long time and who were already contaminating it with unacceptable Anglicisms. If you want to use a good approximation of East Ulster Irish as it was spoken when still vigorous, you should first read all the literature and folklore of the whole of Ulster and then introduce East Ulster elements.
The most quintessentially East Ulster element is, obviously, chan for “not”. It is also Scots Gaelic. If you want to incorporate East Ulster elements in your Irish, you are advised to use it. Basically, chan is like ní, but when used with present forms, it gives them the additional sense of future tense. This is why you should not combine chan with a future form.
Chan is the form used before vowels as well as the mute fh-. Thus: chan aithníonn, chan fhuil, chan fhulaingíonn, chan fhosclaíonn (note that oscail!/oscailt is foscail!/foscal in Ulster). And of course, this suggests that cha, chan lenites the following verb. However, there are certain important exceptions:
cha eclipses verb forms beginning with d or t;
cha does not affect a s- either way: cha samhlóinn a leithéid “I couldn’t imagine anything like it” (or, if you want to sound more authentically Ulster Irish: cha samhlóchainn a leathbhreac).
cha frequently (but not exclusively) eclipses the b(h)- of the forms of the verb “to be”. Thus: cha mbíonn or cha bhíonn, cha mbeadh or cha bheadh, cha mbíodh or cha bhíodh.
On the other hand, while ní irregularly eclipses fuair “found, got, acquired” (ní bhfuair), chan regularly lenites it: chan fhuair.
When there is an independent/dependent form opposition, cha is followed by the dependent form: cha raibh (although many in Ulster would prefer the spelling cha rabh). Or is it? The question is more complicated. In East Ulster folklore, you see forms such as chan gheobhann, which seems to be wildly wrong: to start with, it’s an absolute form, although dependent forms should be used after such particles as go, ní, nach, chan, and moreover, it is a combination of future (gheobhaidh) and present (faigheann, or why not even gheibheann, although the historically correct absolute form is gheibh – faigheann is originally just the dependent form, used after those particles).
The reason behind this awkward-looking form is, as I pointed out above, that the present form acquires a future meaning after cha(n). Cha cannot be followed by future forms, because cha + present already has the additional future sense. Thus, cha bhíonn (or cha mbíonn) stands both for ní bhíonn and for ní bheidh. It seems that it feels important for some speakers at least to code those two meanings into the verb itself by using a combination of future and present forms. In comparison, the formally correct chan fhaigheann probably does not feel future enough.
Before a regular past tense, cha(n) obviously has the form char, which lenites the verb, the same way níor does. Thus, char cheannaigh, char chaith, char thoisigh (in Ulster, toisigh/toiseacht rather than tosaigh/tosú) and so on.
For irregular verbs, note the following past tense usages:
abair – I tend to think that in genuine Ulster Irish it’s char dhúirt or char ‘úirt rather than cha ndúirt. But I might be mistaken.
beir – char rug (not that there is much difference in pronunciation between cha rug and char rug anyway, but the convention is to keep the -r)
bí – cha raibh (or cha rabh – rabh corresponds the pronunciation even in Connemara, but it is traditionally used only by Ulster writers, I’d say)
tabhair – cha dtug – but note that the autonomous form is char tugadh
tar – cha dtáinig (I am not saying char tháinig is wrong, but in Ulster Irish, tháinig usually takes the -r-less particles)
téigh – cha ndeachaigh, cha dteachaigh. The first one is acceptable in the standard language, but in Ulster the past tense dependent stem is usually perceived to begin with t-, thus note forms such as go dteachaigh, nach dteachaigh too, if you are a dialect enthusiast.
Now, if you are all about reviving East Ulster Irish, please use chan, cha, char wherever you’d use ní, níor, but of course not with future verb forms. But if you want to use the cha particles in a way that is largely acceptable in Donegal too, use it only when answering to a statement. Thus:
An bhfuil Ian Paisley ina Uachtarán ar Éirinn? Níl.
An é Ian Paisley Uachtarán na hÉireann? Ní hé.
Is é Ian Paisley Uachtarán na hÉireann. – Chan é!
Tá Ian Paisley ina Uachtarán ar Phoblacht na hÉireann. – Chan fhuil!
Ní hé Ian Paisley Uachtarán na hÉireann. – Chan é, leoga.
Níl Ian Paisley ina Uachtarán ar Phoblacht na hÉireann. – Chan fhuil, leoga.