The Curia building that is now shown in the forum incorporates the remains of several generations of the main building, the Senate meeting hall, in the ancient Roman Senate compound. The original structure built by Tulius Hostilius, Rome's third king (672-640), was a simple structure with wooden benches for the Senators. There were undoubtedly regular repairs and modifications over the years, but a fire in the forum in 80 BC completely destroyed the Curia Hostilia. It was rebuilt by Sulla, the dictator who had resigned and restored the Republic the previous year, but Sulla's building was destroyed in riots after the murder of the demagogue Publius Clodius Pulcher in 52 BC.
Sulla's son, Faustus, started another reconstruction, but that effort was preempted by Julius Caesar, who tore down what Faustus had built and started a much grander complex in 44 BC. While that construction was in progress, the Senate met at the "Curia Pompeia" in the massive temple/theatre complex Pompey had built in the Campus Martius. It was there that Julius Caesar was assassinated on the Ides of March. It was left to Augustus to finish the new Senate buildings in the Forum, which were henceforth known as the Curia Julia.
The Senate burned again in 64 AD in Nero's famous fire and was rebuilt and rededicated by Domitian in 94 AD. Domitian's reconstruction lasted until yet another fire in 283 AD. Diocletian dedicated his own reconstruction in 303 AD. There were numerous subsequent alarums and vicissitudes, but Diocletian's main building, the Senate meeting room, is in remarkably good condition today, due to the fact that, like the Pantheon, it has been in almost continuous use as a Catholic church since medieval times -- first as the church of Saint martin and from 630 AD until 1935 as the church of St. Hadrian the Martyr. The last major restoration was from 1935, when St. Hadrian's church was desacralized, until 1938.
What you see today is essentially Diocletian's Senate hall built on earlier foundations. It still follows the architectural dictates of Vitruvius: its width (18 meters) is two-thirds of its length (27 meters), and the height of its walls (22.5 meters) is half of the total of its length and width. The marble inlaid floor dates from Diocletian's reconstruction as does the dimly visible wall fresco of a "suovetaurile", a ritual slaughter of a pig (sus), a ram (ovis) and a bull (taurus) and the stepped platforms on both long sides where sat the chairs of the Senators. The curved apse, which was at the rear (north) of the hall, was flattened when the curia became a church.
The rest of the senate complex is missing. Immediately to the west of the Senate meeting hall was a colonnaded courtyard in which stood a small temple. West of that was the secretarium, about half the size of the main chamber, where closed meetings and clerical work took place. (Only senators, guests, invited speakers, and official scribes could enter the main hall, but the doors traditionally were left open while the Senate met, and official representatives of the popular committees and other spectatori and auditori gathered on the porch and in the comitium area immediately in front of the Senate.) In later phases there was a portico or pillared porch across the front of the entire complex and the rows of square holes on the front of the building today are probably where the portico was attached. Contemporary accounts say that the lower half of the Curia was covered in white marble and the upper half in stucco. The bronze doors are copies of the doors commissioned by Julius Caesar and installed by Augustus. The originals are now the main doors of St. John Lateran, having been moved there by Borromini.
On display inside the Curia today, but not part of the original structure, are the Plutei Traiani, which are carved stone balustrades which were placed by Trajan either on the edge of the rostrum or on the sides of the black pavement marking the underground "Tomb of Romulus". Although the archeologists can't decide exactly where Trajan erected them, they are of great historical value because the carvings show the full length of both sides of the forum at the time they were erected.
http://library.thinkquest.org/11402/curia.htmlForvm Romanvm Curia site -- includes a drawing of Diocletian's reconstruction
http://www.ukans.edu/history/index/europe/ancient_rome/I/Gazetteer/Places/Europe/Italy/Lazio/Roma/Rome/Forum_Romanum/.Texts/Huelsen*/2/19.html best description (but in Italian), and plan showing construction phases
http://www.seindal.dk/rene/sights/sight/180.htm Curia pictures
http://sights.seindal.dk/sight/335_Plutei_of_Trajan.html The Plutei of Trajan, now inside the Curia