There's been lots of research into this, and for in the 70s and 80s this was the subject of a major debate in the academic community. With the dust of that debate having settled down, the consensus is that though Roman expansion wasn't planned, it was deliberate. There wasn't a grand strategy, set out by the Senate or whatever, which determined where Rome would expand. Instead, Roman expansion was a result of societal factors, the three most important ones being a real but unjustified fear of being sacked (again), a greedy elite, and individual's quest for glory.
Most of Rome's expansion took place during the Republic. My answer here will focus on the early and middle Republic, with a brief mention of the Late Republic.
In histiorography, there have been three distinct views of Roman wars of expansion: defensive imperialism, aggressive imperialism, and individualistic imperialism (this last one is not the proper term but it fits nicely with the others :). I'll discuss each for a bit (taken from this post I made under my previous name).
Defensive Imperialism
The notion of 'defensive imperialism' really got started in the second half of the 19th century. It is no coincidence this happened then, as the 'defensive wars' of Rome mirrored the wars of unification in Germany and Italy. If Rome was justified in fighting for the unification of the Italian peninsula, surely so were Germany and Italy justified in fighting for their unification. The German historian Theodor Mommsen argued that Rome was merely fighting to maintain the status quo; that Rome wasn't driven by a desire to expand, but that it was a case of conquer or be conquered. Note that in this view Rome acts much like a nation state: a single actor, acting rationally. 'Defensive imperialism' was the main school of thought among ancient historians throughout the early 20th century. Look for works by Maurice Holleaux and Tenney Frank to find nice examples.
Aggressive Imperialism
In the second half of the 20th century, things began to change. The Western empires had fallen or were in decline. There no longer was a need to justify these empires using the ancient Roman example. The main view even went the other way. As the expired modern empires were viewed more negatively ('imperialism' became a bad thing instead of a good thing), so too was the Roman empire [I'm using 'Roman empire' here a bit imprecise, referring to expansive Roman Republic, which in this view behaved like an empire, instead of the - later - Roman Empire proper).
At the end of the 1970s William Harris published a book, War and Imperialism in Republican Rome 327-70 BC, in which he argued that not defense and security were behind Rome's warmaking, but social and economic factors. In short, war was profitable. It led to glory and power, to riches and profits. This view quickly gained prominence, but not without debate. For one thing, it was critisized as being too single-minded just like the 'defensive imperialism' notion.
Individualistic Imperialism
As glory, power, and profits came into play, the importance of individuals in the warmaking was highlighted. No longer was Rome as a single actor doing something, but it was Roman society, a collection of individuals, valueing these things. This idea was extended in the 1980s, most notably by Arthur Eckstein in his book Senate and General: Individual Decision-making and Roman Foreign Relations 264-194 BC. Eckstein examined many of the wars in that period. He looked at the instruction generals (consuls or praetors) received from the Senate and what the generals actually did while in the field. He found that the generals had a large amount of freedom to do as they saw fit. Attacking cities, making peace treaties, provoking wars, it all happened. In theory all actions of the general had to be approved by the Senate at the end of the year, after the general returned to Rome, but Eckstein found that this was just rubber stamping. In all those years, it happened only once or twice that the Senate did not approve.
This close examination of what generals did shows that you can't really talk of Rome doing something. Once the Senate sent out an army, the general had such a large degree of freedom that the Senate had very little say in what happened. Note that the Senate was fine with this, as all generals were senators, elected by the other senators and if the current general could do pretty much what he wanted, so too could next year's general, which would be another senator. Even if a senator missed out this year, he - or someone he's close to - could be up next. (I found the same dynamic at work in the period 218-133 BC.)
Incorporation of areas into the empire
The above explains why wars were fought, it does not explain how areas were incorporated into the empire. Here too, a very nuanced view has emerged, with attention to differences between areas.
At first, Rome didn't do anything really with conquered territory. Within Italy, subjugated cities came under the Roman sphere of influence but kept a large amount of independence. After the First Punic War, with the first expansion overseas (Sicily and Sardinia) things began to change. Rome started sending praetors to govern these areas. Praetors were elected and assigned a duty every year. Two of them were assigned to Sicily and Sardinia respectively. After the conquest of the Iberian peninsula (Spain) in the Second Punic War that area was assigned to two praetors as well, each with their own area of responsibility. It is from the areas these praetors governed that provinces emerged.
In Greece, things were much different. There Rome for many decades was satisfied with having a sphere of influence and letting cities govern themselves. Macedonia, Rome's long-time enemy, was placed under a praetor though. Greek cities which rebelled against Rome often lost their independence and were placed under the Macedonian province. It's only in the late Republic that Greece became a province in and of itself. In other areas much the same applied: where possible Rome was satisfied with just having a sphere of influence (with "independent" allies), where needed Rome sent a praetor or consul to take direct control.
In the Late Republic the system was reformed: Rome started using proconsuls (former consuls) to govern provinces. There are others in this sub who can explain the how and why of this better (it's just after my area of expertise).
I hope this answers makes clear how Roman expansion worked. If you have any questions, do let me know!
Works mentioned:
Other interesting reads:
The first couple of chapters of The Cambridge Companion to the Roman Republic, edited by Harriet I. Flower (New York, 2004):
These works by Rosenstein: