I know more about Edward's Army than Llywelyn's, but this is from an old essay I wrote about the conquest.

Before the declaration of war in November of 1276 Llywelyn had reached the zenith of his power. He controlled over three quarters of Wales, from Anglesey in the north to Machen in the south and Cydwel in the West to Chester in the East with nearly 200,000 subjects under his dominion.
Arbitration had been sought by Llywelyn with the King of France in the Summer of 1276 but by that time Edward was determined to go to war. The main muster of the feudal host was called by Edward to occur in Worcester on July 1, 1277. While preparations were being made Edward appointed Roger Mortimer to protect the marches from the city of Montgomery, Payn de Chaworth at Carmarthen and the Earl of Warwick was to do the same from Chester. Before Edward began his march in Northern Wales his commanders had huge successes in the South and the East of Wales. The Earl of Lincoln retook Bauseley, Gruffydd ap Gwenwynwyn and Llywelyn’s brother Dafydd negotiated the surrender of several Welsh Lords and Peter Corbert gained the surrender of Godwrr. On July 1st when the feudal host was to set out the Welsh lords Rhys ap Marededd, Rhys Wynded, Cynan ap Maredudd ap Owain and Rhys Fuchan all surrendered to Edward.

Edward’s army was made up of 228 knights and 294 sergeants who all were serving their feudal obligation of 40 days without pay. Knights at the time wore a shirt of mail called the hauberk, iron greaves, back and chest plates that would be made of hardened leather or steel, mail leggings known as chauses with a surcoat often worn over it all, by the end of the 13th century knights were moving from round caps to fully enclosed flat-topped pot helms. The mail provided the knight with more maneuverability than later suits but was more susceptible to crushing sword blows and arrows. English foot soldiers at the time would have carried a sword with a flat blade that was designed for hacking rather than stabbing. A legal record during Edward’s reign described a more ornate Cologne sword with a 45 inch blade, a 5 inch hilt with a steel pommel, and maple wood inlaid in the handle. When Edward’s army reached Rhuddlan it was comprised of nearly 15,000 soldiers, of whom 9000 were Southern Welshmen. For the supply of the army Edward also requested 200,000 crossbow bolts to be made. The Southern Welsh favored the bow while their counterparts in the North fought Edward with the traditional long spear. The longbow became an integral part of Edward’s armies; the bow itself was described in a legal document as made of Spanish yew with a circumference of six inches at the middle and having a total height of an ell and a half, roughly a man’s height. With a draw between 100 and 175 pounds the longbow was accurate within a range of 200 yards, and a good archer could shoot upwards of 20 arrows in a minute. In Edward’s army knights were paid 2 shillings a day, sergeants received 1 shilling, and infantrymen received 2 pennies.

From Worcester Edward moved his force North to Chester where the fleet of 26 ships from Cinque Ports had answered his feudal summons to supply the men as they marched West. 1800 laborers were employed by Edward to cut a swath through the forest from Flint to Rhuddlan so Edward could move his army through while at the same time 530 men worked in Flint on fortifying the city with a great ditch. The laborers were escorted by crossbowmen and archers from Edward’s army. Llywelyn never risked open war as he did not have the forces to be successful; instead the skilled North Welsh spearmen exercised guerilla tactics against Edward’s men. Edward dared not attack Llywelyn’s mountainous fortress of Snowdonia, instead electing to move along the north coast from Rhuddlan to Deganwy. Edward then sent his men to collect the harvest from Anglesey and cut Llywelyn off from his supplies. Cut off from his supplies and being badly beaten on all fronts Llywelyn had no choice but come to terms in a humiliating surrender in November of 1276.

The surrender was a difficult for Llywelyn to cope with; he was fined 50,000 marks by the crown, he paid 2000 at the negotiations but the indemnity was so large it seems that it was more to symbolically to indicate the weight of his crimes. Llywelyn was allowed to retain the princely title but that was almost a humiliation as most of his lands had been taken away, two of the four cantrefi went to Edward, two went to Llywelyn’s brother Dafydd and Llywelyn’s brother Owain was given Llyn.

Sources:

Edward I by Michael Prestwhich Edward I by L.F. Salzman Age of Conquest by R.R. Davies A History of Wales John Davies Armies and Warfare in the Middle Ages by Michael Prestwich Calendar of the Close Rolls