Great Question!
So throughout the principate, any standard Roman Legionaire had to complete a total of 25 service years. These years were divided into 5 years of active duty with 6 months as "rest". During these rest months what would often happen was that the legion would be called back from the front. New men would be put in the legion to refill its lost ranks (A legion may lose men due to a plethora of reasons including desertation, disease, and simple war). This also ensured that a single legion would never get overextended much in the same way how American units are deployed for "tours" but then recalled.
But as you would imagine not every soldier managed to complete the given 25 years in the army. The Army officially recognized three different types of discharge. Soldiers who became unfit due to sickness or injuries were released from service with a "Conditionarry honorable discharge" (Latin: missio causaria). This was not done lightly but only after 2 certified army health professionals had confirmed that it was impossible for a man to serve at full capacity were they allowed. There are even records of Tribunes not allowing immediate dismissal on active fronts instead of simply offering the injured men easier jobs (such as weapons maintenance) until reinforcements arrived.
There was also the Dishonorable discharge (missio ignominiosa). This was the penalty for soldiers committing a serious crime. Such men were barred from the law from living in Rome itself or from entering the Imperial service of any form. Beginning from the period of Tiberius, they were even tattooed. These men were also granted none of the rights and the privileges that a soldier who was honorably discharge get.
Finally, there were the honorably discharged soldiers (Honesta Missio). These men were given a lot of benefits by the Principate this included (referring to your question) a Pension. Officers were also oftentimes given a piece of land. The size of which depended on the rank of the officer. Medically discharged soldiers enjoyed in many ways the benefits of an honorably discharged men although it can be noted that their grants were usually scaled in accordance with their length of service.
The Army kept complete documentation of man (including to some extent what he did in his civilian life). Any man would have to keep in contact with the military five years after his discharge. This was likely so that if need be these men could be recalled in cases of emergencies. (It is important to note that veterans had complete military training). If recalled they would not serve on the frontlines but serve as primarily 'supporting legions' i.e building roads and helping in the maintenance of large forts.
The type of discharge was marked against a man's name in his unit's record. The soldier received a written statement of release which documented the length of service, the branch of service and the date of release. Dr.Adrian Goldsworthy does mention one such find in his book The Complete Roman Army
The form dating to 4th January AD 122 confirming the discharge of Lucius Valerius Noster, cavalryman from the turma of Gaius in Ala Vocontrium.
In his book, Edward Gibbons mentions that a Primary reason for the failure of the military in later antiquity was the fact that the men and the officers were never as experienced. He points out that this was mainly due to the fact that entire groups of soldiers could file a formal "mistreatment accord" against their officers and choose early discharge as the form of compensation. Gibbons notes that this became increasingly common later on.
Unfortunately, the sample evidence of what legions did after discharge is tiny. So many factors determined the men eligible for discharge and it would be unfair to assume that all of them chose a similar path.
Tacitus does note however that a good number of men chose to live near their old base taking up residence near the vicus. Many soldiers married local women after their discharge and then remained in the original province. Oftentimes their sons went on to join the army.
As it is the case today, there came a certain pride after completing an honorable term in the army. Men continued to associate themselves with their units decades after their original service had ended. As I have stated before army men had privileges after their service. They were exempt from many types of punishments and commanded greater respect within their localities. The pension continued to fund the soldiers' everyday life. It is recorded that during Caesar's time it was 2 Denarii per 4 months (Recorded by Caesar himself). Though it would have been paid in the much more convenient silver. Tiberius increased it to 3 Denari and then Domitian to 4. (Recorded by Tacitus). This was a decent amount of money and would fund any modest lifestyle though the officers were given land and slaves as well and often would become "farmers" of sorts. Some men even became merchants.
Auxillary veterans were nowhere near as prestigious as Legionary Veterans. Although even they had benefits, the most defining of which was that after an honorable service they (and by extension) their children were declared Roman citizens. This indeed came with a lot of benefits.
Soldiers would also get different burials in honor of their service to Rome and the Emperor.
I hope I was able to answer you!
Sources:
For Further Research I'd Recommend:
http://scholar.google.com.pk/scholar?cluster=5605261588351864303&hl=en&oi=scholarr
^((Research Paper by Nash Williams.))