Even though I vaguely remember my linguistics course from college, I was completely confused by references to the 'genetive case' or the 'genetive plural' in my textbooks. There wasn't any real explanation of it.

Actually, using the genetive case pretty easy, and Irish has a few rules about it.

Rule 1: A noun is in the genetive case if it is preceded by another noun.
mo dheartháir — my brother
bean mo dhearthár — my brother's wife (lit., woman of my brother)

Rule 2: When used as a 'verbal noun', one that usually ends in '-ing' in English

Rule 3: As part of a compound preposition
an siopa — the shop
os comhair an tsiopa — in front of the shop

Rule 4: After chun (to), cois (beside), timpeall (around), and trasna (across)
an tír — the country
timpeall na tíre — around the country

Rule 5: After words that denote quantity
airgead — money
a lán airgid — a lot of monoey

Rule 6: After the word cuid used for unspecified quantities
gruaig — hair
mo chuid gruaige — my hair

There are a few noticeable changes for the genetive case, although sometimes the words look just like they do normally.

	masculine	feminine
starting with consonant	retain lenition	remove lenition
starting with the letter s	add 't'	remove 't'
starting with a vowel	remove 't-'	add 'h'

The article 'na' is used instead of 'an' for singular feminine nouns.

Here's a quick outline of how to guess what the genetive form may be for a specific noun:

masculine nouns	feminine nouns
change the final consontant from broad to slender	change the final consonant from slender to broad and add -ach.
replace -ach with -igh	replace -ach with -i
add -a	add -e