How to differentiate the Irish dialects?

There are a number of distinct dialects of Irish. Roughly speaking, the three major dialect areas coincide with the provinces of Munster (An Mhumhain), Connacht (Connachta), and Ulster (Ulaidh).
Munster dialects

Munster Irish is spoken in the Gaeltachtaí of Kerry (Ciarraí), Coolea (Cúil Aodha) in the western part of County Cork (Contae Chorcaí), and the tiny pocket of Irish-speakers in An Rinn near Dungarvan (Dún Garbháin) in County Waterford (Contae Phort Láirge). The most important subdivision in Munster is that between Decies Irish (spoken in Waterford) and the rest of Munster Irish.
1. The use of personal endings instead of pronouns with verbs, thus "I must" is in Munster caithfead, while other dialects prefer caithfidh mé (mé means "I"). "I was and you were" is Bhíos agus bhís in Munster but Bhí mé agus bhí tú in other dialects.
2. In front of nasals and "ll" some short vowels are lengthened while other are diphthongised.
3. A copula-construction involving is ea is frequently used

Connacht dialects

The strongest dialect of Connacht Irish is to be found in Connemara and the Aran Islands. In some regards this dialect is quite different from general Connacht Irish but since most Connacht dialects have died out during the last century Connemara Irish is sometimes seen as Connacht Irish. Much closer to the traditional Connacht Irish is the very threatened dialect spoken in the region on the border between Galway (Gaillimh) and Mayo (Maigh Eo). The remnants of the Irish of Tourmakeady (Tuar Mhic Éadaigh) in southern Mayo and Joyce Country (Dúthaigh Sheoige) are considered the living Irish dialects closest to Middle Irish. The northern Mayo dialect in Erris (Iorras) is in grammar and word-building essentially a Connacht dialect, but shows an affinity in vocabulary with Ulster Irish.

Connemara Irish is very popular with learners, thanks to Mícheál Ó Siadhail's teach-yourself textbook Learning Irish. However, there are features in Connemara Irish which are not accepted standard, notably the preference for verbal nouns ending in -achan, such as lagachan instead of lagú = "weakening". The non-standard pronunciation with lengthened vowels and heavily reduced endings give Connemara-Irish its distinct sound.

Ulster dialects

The most important of the Ulster dialects today is that of the Rosses (na Rosa), which has been used extensively in literature by such authors as the brothers Séamus and Seosamh Mac Grianna, locally known as Jimí Fheilimí and Joe Fheilimí. This dialect is essentially the same as that in Gweedore (Gaoth Dobhair), the same dialect used by native speaker Enya and her siblings in Clannad.

Ulster Irish sounds very different and shares several in Ireland unusual features with Scots Gaelic, as well as having lots of characteristic words and shades of meanings. However, since the demise of those Irish dialects spoken natively in what is today Northern Ireland, it is probably exaggerated to see Ulster Irish as an intermediary form between Scots Gaelic and the southern and western dialects of Irish. Indeed, Scots Gaelic does have lots of non-Ulster features in common with Munster Irish, too.

One noticeable trait of Ulster Irish is the use of the negative participle cha(n), in place of the Munster and Connaught version ní. Even in Ulster, cha(n), most typical of Scots Gaelic, has ousted the more common ní only in easternmost dialects (including the now defunct ones once spoken in what is now Northern Ireland). The practice seems to be that cha(n) is most usually used when answering to a statement, either confirming a negative statement (Ní aon mhaith ann - Chan fhuil, leoga = "It is no good" - "Indeed it isn't") or contesting an affirmative one (Tá sé go maith - Chan fhuil! = "It is good" - "No, it isn't!"), while ní is preferred in answering a question (An bhfuil aon mhaith ann? - Níl = "Is it any good?" - "No"). (From www.irelandinformationguide.com)