I'll break this question up into two sections: urban and rural life.

Urbs, Sweet Urbs: Urban Life in the Roman Empire

While other cities in the Roman Empire did grow to impressive sizes (Alexandria had around half a million people or so living there at its height), most Roman cities were smaller, between thirty and two hundred thousand inhabitants. These cities still had standard features: aqueducts, public baths, and large fora for commerce and trade, as well as military garrisons that protected the nearby countryside and could resupply the legions on their campaigns. Often, cities imported food after outstripping the production of the nearby countryside. While few were as pronounced as in Rome, many still relied upon grain imports to forestall famine. This reliance on external supply lines constitutes a major reason for why the Crisis of the Third Century caused deurbanization, since disruptions in the countryside and elsewhere in the empire would interrupt shipments to many cities.

During the Pax Romana, most cities tore down their walls for building materials or to open up more land for settlement as they grew. Many cities retained a somewhat distinct local identity thanks to admixture from local populations and Roman colonists. All Roman cities contained large slave populations, though none to the same extent as Rome itself. Workshops and trade were the primary professions for most inhabitants, slave and free, with the wealthiest being the local equestrians (Roman citizens owning property in excess of 100,000 denarii), who would be the senior administrators and local civic leaders. Most cities were governed by an internally-elected city council that conducted major religious festivals and maintained public spaces. Most monumental construction, however, was done by local notables or people from the town who made it big and now lived in Rome. Pliny the Younger, for example, donated a school to his hometown of Como so that other youths in the city could receive an education free of charge. Patronage helped ensure that even relatively small towns and cities could have the same amenities as larger cities.

In the Western Mediterranean, most cities grew out of Roman colonies, such as Narbo (modern Narbonne) in southern Gaul, or existing tribal settlements, like Lutetia (modern Paris). Some notable exceptions include the cities of Massalia (modern Marseilles) and Carthago Nova (modern Cartagena), which were long established cities in their own rights. New cities followed a standard, rectilinear plan centered on the two primary streets: the north-south cardo and the east-west decumanus. At the intersection of these streets would be the primary civic buildings, like baths and the forum, as well as any other administrative buildings. As a general rule of thumb, once a city reached a certain size (around 50,000 inhabitants), a new settlement would be created somewhere else. First and foremost, these cities were market towns, where goods from the countryside could be sold into the larger trade networks of the Roman world.

In the Eastern Mediterranean, the story was much different. Most of the time, the Romans were dealing with established urban centers stretching back centuries. These cities were large and had vast domestic industries, as well as often being major trading centers. Cities like Antioch often received direct Imperial patronage in the form of baths, arenas, and hippodromes. Many cities maintained their own laws and legal systems (though Roman citizens were always tried according to Roman law by Roman magistrates), and the city councils, possessing more money, operated on much grander scales than their western counterparts. During his governorship in Bithynia, Pliny the Younger writes about the city of Nicomedia attempting to build an aqueduct twice, once for over 300,000 denarii, another time for over 200,000 denarii, as well as attempting to start a municipal fire brigade. Many governors worried about (or even partook in) corruption in these cities, but the vast wealth made them indispensable to the Romans.

Ager Publicus: Living in the Roman Countryside

Depending on what part of the Roman Empire we're talking about, rural life would look very different. Time also plays an important factor: in the time of Augustus, slave labor was very common in the countryside, but by the second century CE, many had begun to transition to a tenant system. There are several reasons for this, including the gradual diminishing of the slave population (thanks to both manumission and the cruel living conditions for many slaves). Most Roman slaves were taken in war, so peace within and without (relatively) meant a much smaller population. The settlement of veterans also contributed to a growing rural population of free citizens that worked the land independently.

In areas of northern Hispania, Gaul, and Greece, the primary rural population would be free citizens working the land with the aid of a few slaves, if any, with villas dotting the landscape where wealthier landowners would maintain larger slave work forces to cultivate the land. These areas produced mostly raw materials, like lumber and clay, as well as foodstuffs, like vegetables, fruits, meat, and cheese to the cities. In Greece, these farms produced olive oil and wine, while in Gaul they raised livestock like cows and pigs. Most farms operated on a subsistence basis.

In Egypt, Italy, and southern Hispania, the landscape was dominated by the latifundia, large slave plantations owned by wealthy Romans, with work forces numbering in the thousands. Many latifundia arose from the bankruptcy of smaller landowners, primarily soldiers who had little knowledge of farming. Senators and wealthy locals would then buy out the farms and turn it over to their slaves to cultivate. The latifundia, like the independent farms, produced olive oil and wine for export, being mostly self-sufficient. In Egypt and Sicily, the latifundia produced much of the Empire's grain supply.

I hope I've answered your question. Feel free to ask for clarification or more details if you'd like.