Trinity Force is typically your core item. After it has been completed, you generally want to focus on CDR, Armor, MR, Health, and Attack Speed depending on team compositions. Irelia's damage starts falling off a bit late-game, so you'll generally want to get 2 damage items if possible. A normal build may look something like (in no particular order):
or
or
,
,
,
,
, 
Frozen Heart and Spirit Visage provide a nice increase to your durability (Health, Armor, MR, increased healing) and give 30% CDR. CDR increases the uptime of your W and your sticking potential (Q, E) significantly.
Other common purchases may include:
Used as an alternative Tenacity item, commonly against AD or AA heavy teams so that you can purchase Ninja Tabi.
Provides sustain and on-hit percent current health damage which improves your ability to fight tanks and stick to squishy targets. Offers a nice increase to damage and sustain.
A good pick-up when snowballing against squishy teams to provide a short-term boost for assassinating squishies.
A good pickup for a mix of damage and survivability against AP heavy teams. It doesn't offer attack speed, but the MR and shield can be quite valuable against certain team compositions.
The alternative to Maw of Malmortius. It provides more useful offensive stats or Irelia while sacrificing the magic damage shield.
Very useful for waveclear and splitpushing,, providing good sustain and a burst of damage.
Great pickup against AA-heavy teams, since the reflected damage combined with your sustain can make you quite difficult to kill.
Covered in a bit more depth since I saw you question it elsewhere.
Armor Pen is actually pretty decent on Irelia due to the constant Spellblade procs and the high base damage on your ultimate. It's very nice for bursting down squishy champions like the ADC or APC.
The big things about Youmuu's Ghostblade are:
- it is extremely cost efficient when the active is in use, which can offer a burst of power
- it gives 25% critical strike chance when combined with Trinity Force, increasing your sustained damage
- The 20% movement speed is great for chasing down targets or escaping
It's a situation item that can be purchased when you are snowballing and don't have to worry about killing the enemy tanks.