Yom Ha’atzmaut is not quite a festival. While today may well be a big day for many children in Jewish schools which annually celebrate Israel’s birthday, it has yet to take its place on the religious calendar in the same way as Chanukah or Purim.
Some Anglo-Jewish synagogues may hold special services of thanksgiving but it is by no means the norm.
There is no set liturgy. The latest edition of the Singer’s Prayer book for the Chief Rabbi’s congregations notes Hallel is recited in “most communities” in the morning service (just as on Chanukah, because of events which took place in the land of Israel, but not on Purim).
Still, some religiously hedge their bets by reciting Hallel without the accompanying brachot. In view of the unresolved conflict between Israelis and Palestinians, perhaps the most appropriate custom would be to recite a half-Hallel with blessings.