The Dagor-nuin-Giliath (Battle-under-Stars) was the second battle of the Wars of Beleriand, but the first fought by the Noldor. Or The battle began when the Noldor of Fëanor had arrived unexpectently at the Firth of Drengist, and passed through the Gate of the Noldor into Hithlum. They encamped on the northern shore of Lake Mithrim.
Morgoth hoped to destroy the Noldor before they could establish themselves, and sent his forces through the passes of the Ered Wethrin. Although the Orcs of Morgoth by far outnumbered the Ñoldor, the Noldor were still empowered with the Light of Valinor, and quickly defeated them. The Orcs retreated north through Ard-Galen, with the Ñoldor in hot pursuit.
The forces of Morgoth that had been besieging the Havens of the Falas since the First Battle of Beleriand marched north to attack the Ñoldor in the rear, but a taskforce led by Celegorm ambushed them at Eithel Sirion. Trapped between the two Noldorin forces, the Orcs fought unendingly for ten days, encircled at the Fens of Serech. All but a few Orcs perished, and Fëanor in his wrath pursued even this small group. The tables turned at the edge of Dor Daedeloth, as Balrogs poured forth from Thangorodrim. Fëanor stood his ground and long fought alone, until he finally fell. Then the armies of his sons reached him, and the Orcs and Balrogs retreated. Fëanor died in sight of Angband, thrice cursing Morgoth.
Immediately following this the Moon rose, and with the rising of the Moon Fingolfin and the second, greater Host of the Ñoldor arrived in Lammoth. There they were attacked by Orcs which had been sent there by Morgoth to attack Fëanor in the rear, and they fought their first battle, the Battle of the Lammoth. The Ñoldor were caught off-guard, and Fingolfin's son Argon was slain. Fingolfin and his host pursued the Orcs until they were completely destroyed, and then passed into Mithrim as the Moon first rose.
It was thus a bittersweet victory for the Noldor, as they had destroyed most of Morgoth's forces in one strike, but their greatest leader had been mortally wounded, and they had lost one of their princes.
(The Battle of the Lammoth and Argon do not appear in the published Silmarillion at all, because they only came to light in very late writings by Tolkien. In the published Silmarillion Fingolfin's host only arrives after the battle is long over.)