As the boxes of votes are opened, an estimate of the votes for each candidate will be revealed as party tallymen mark down the first preference votes for each candidate. The early tallies will be available by about 10:30pm, but this won't give the full picture. The full tallies of each constituency will usually be available by about 12 noon.
The first counts should start to roll from about 3pm onwards, running up until teatime. Crucially, this will give the first accurate picture of how each candidate has fared. Expect a number of Fine Gael and Labour candidates to be elected on the first count.
Be prepared to stay awake beyond midnight. The second count is usually the distribution of the surplus of the poll-topper, which invariably goes to their party running mate. So this often tells you little enough about the destination of the final seats. The third count is usually the elimination of the weakest candidates. The fourth count is where it gets really interesting because you start seeing substantial candidates being eliminated with a lot of transfers to distribute.