Prior to the Marian Reforms (107 BC), Roman Legions were primarily comprised of conscripts (the word Legion actually derives from the Latin word for conscription/selection). This was limited to able-bodied, property-owning Roman Citizens. Soldiers paid for their own equipment, which dictated the formation and structure of the legion. The poorest folk who could not afford to properly equip themselves formed the Velites, a light infantry usually tasked with skirmishing, raiding, and harassing the enemy. The heavier main infantry were wealthier men, but not the wealthiest, who could afford proper gear. These soldiers formed three ranks based upon experience called Hastati, Principes, and Triarii, from least to most experienced. The wealthiest men, those who could afford horses, formed the cavalry known as the Equites. These men were usually wealthy enough to become influential in later life, and might be likened to the later Equestrians of the Imperial period.
The Legion has about 5,000 men on average, with about 3/4 heavy infantry and 1/4 Velites, give or take. It was broken into Maniples, a unit comprised of two Centuries. A century was a unit of 100 men commanded by a pair of Centurions, junior and senior. Maniples themselves tended to have local maneuvering autonomy in battle (or the most autonomy that was possible in such a battle) and were largely responsible for the success the Romans had against the Greek Phalanx formation.
There is a decent amount of debate among historians as to how ancient battles actually played out, but in general the Roman legion would bunch up into a block, or several blocks depending on the situation, and use their superior heavy infantry to defeat the enemy. The Greek Phalanx, a similar block formation, was quite formidable but stood little chance against the Maniples of the legions, since a Maniple could break off from the main line and pursue an objective, something not allowed in a phalanx. Roman Cavalry is generally regarded as poor, and tended to prefer shock-and-awe charges rather than more sophisticated tactics.
The legion tended to construct fortified camps on the march (remember pre-Marian legions were not standing, but temporary) and would drill when necessary, but not as much as the later Standing Legions were prone to do. The camp was always laid out the same way, making for easy construction and break down, and easy of navigation in the camp. Much like the Roman people, the legion was quite good at logistics and organization.
Most of this comes from Polybius, a Greek hostage in Rome who wrote extensive histories.