The Lebanese Army (not Hizbollah) responded with warning shots, then with live fire. The Israeli counter-reasponse apparently killed three Lebanese soldiers and a reporter. A sniper from the Lebanese side of the border then killed "a high-ranking Israeli officer.
Although Israel routinely violates Resolution 1701 (overflights, shelling of Lebanese fishing boats, etc.), Hizbollah has also done so, though less blatantly.
The Israelis are now responding with heavy artillery and rocket fire, as well as white phosphorus. Numerous Lebanese soldiers and civilians have been injured in the exchange, which is probably escalating to include Hizbollah rockets, as I write.
Here's the longest report on this I have found yet, from Iran's Press TV, not always the best source, to say the least:
UPDATE - Wednesday 7:00 a.m: According to information coming out late Tuesday, the Lebanese not only fired first (as reported above), but the "pruning" operation - according to the IDF - had been announced to Lebanese forces and to UNIFIL in advance. If that is the case, the Lebanese Army, not the IDF, violated UN Resolution 1701.