One of the first important battles was that of Cymerau.
In September of 1256, Stephen Bauzan, Prince Edward’s officer in south-west Wales, brought a substantial force of men to Ystrad Tywi, located in the northern portion of Deheubarth at the base of the Cambrian Mountains.
Thus, on the eve of Llywelyn ap Gruffydd’s advance into Perfeddwlad, a force was arraigned against Maredudd ap Rhys Gryg, the Welsh lord of those lands. Llywelyn and Maredudd, eyeing each other with mutual concern about their own power and authority, struck an alliance, and perhaps this is the true impetus for Llywelyn’s foray east of the Conwy River. After he took all of Gwynedd under his control, he swept south, taking over all of Wales from the Dee River to the Dyfi, and then turning southwest towards Ystrad Tywi and taking all those lands for Maredudd.
Then, Llywelyn turned back east and drove towards Welshpool, through the lands of Gruffydd ap Gwenwynwyn in Powys. Further south, he took lands from Roger Mortimer, including Builth, initiating a lifelong animosity between the two men. Llywelyn found himself in possession of almost the whole of Wales and the chroniclers realized he was cut from the same cloth as the great Kings of Wales who preceded him. They began to speak of him in the same breath as his grandfather, Llywelyn Fawr.
All this activity forced Prince Edward to engage his Marcher barons–Mortimer, Bohun, Lestrange, Valence–none of whom was enthused about the idea of challenging Llywelyn. Edward was also short of funds. But he had no choice but to attempt a counter measure and try to wrest back some of the lands that Llywelyn had taken from him.
At Edward’s behest, Bauzan again set out (hard to see why Edward entrusted this mission with him, given the disaster of the previous year, but he did). On 31 May 1257, he reached Llandeilo Fawr and camped. During the night, Maredudd ap Owain and Maredudd ap Rhys drew their forces close. At dawn, they attacked in a shower of lances and arrows. For two days, the English cowered under the onslaught. Rhys Fychan, an ally of Edward and Prince Llywelyn’s nephew, who’d encouraged the whole endeavor, slipped away and made for Dinefwr. This was the Welsh court of Maredudd ap Rhys Gryg, to which he thereby transferred his allegiance.
The next day, the English attempted to retreat to Cardigan, but at Coed Llathen the force lost many of its supplies. Then, at Cymerau, the Welsh and English forces met openly on a battlefield. The Welsh so routed the English that 3000 men were recorded as having fallen. It was an embarrassing and epic defeat for Edward. Unfortunately for Llywelyn, his alliance with Maredudd ap Rhys Gryg was irrepairably damaged by his acceptance of Rhys Fychan back into the fold, and Maredudd defected again to the king before the year was out.
These details come from:
Marc Morris, A Great and Terrible King, Edward I and the Forging of Britain.
J. Beverley Smith, Llywelyn ap Gruffydd.
And Wikipedia has a great description here: http://en.wikipedia.org/wiki/Battle_of_Cadfan#The_Battle_of_Cymerau