There basically were three types of recruitment back then:
1) volunteering, like it is in the Western world today
2) hereditary recruitment
3) fiscal recruitment
Of course it was always possible to call the draft in particularly needy times.
Voluntary recruitment was always possible. Both Roman citizens and Barbarians could enlist, they just had to be free men.
Categories of people who COULD NOT enlist were: Criminals, Cooks, Bakers, Bartenders and other jobs that were considered humiliating (according to the Codex Theodosianus VII.13.8 (380).
There was a form of hereditary recruitment, according to which the soldiers' sons had to enlist as well. This came into effect with a law passed by Constantine in 326 a.D. (Codex Theodosianus VII.22.8)) A lot of soldiers' son would maim themselves in order to dodge service.
Since the two above mentioned types were not sufficient, in the year 352 a.D. a new type was introducted: Fiscal recruitment. In short, if a wealthy land-owner or a rich man could not afford to pay all of his taxes to the government, he could then pick some of his peasants and pay "in recruits". Of course they always picked the weakest guys so this system never proved too effective for the quality of the army.
Another important way of recruitment was the recruitment of the Foederates. What were they? Mercenaries. They would still fight under their Barbarian chiefs but were in fact mercenaries who fought for Rome.
Hope it was useful, Fox.