During the principate legionary and auxiliary pay was generally issued in three or four (after Domitian) yearly installments, and was standardized depending the rank of the soldier in question, so pay was a pretty regular occurrence. As is unsurprising legionaries were always paid more, although the most noticeable disparity was between cavalry and infantry pay. To compensate, however, auxiliaries were generally awarded citizenship upon completing their service, which likely made the empire worth fighting for in the eyes of some.

In addition to this a legionary was granted a fixed amount (12,000 sesterces under Augustus) upon being discharged from the legion after having served the established amount of time (around 20 to 25 years depending on the time). An emperor would also frequently award donatives to his troops as a show of his personal investment in their well being. As a result of all this, the general trend is an increase in all military salaries throughout the early empire. For instance, legionary infantry pay around the time of Augustus was 900 sesterces per year. By Maximinus in the mid 3rd century this had risen to 7,200 sesterces annually

Mutinies did also occur over conditions of service and pay. The death of Augustus sparked several in Germany, part of which was due to the disparity in pay between legionaries and praetorian guards at the time, but also because their salaries as a whole were meager.

This was obviously a huge drain on the emperor's resources, but it was in his interest to secure the loyalty of his troops, particularly the Praetorian Guard, as failure to do so could result in his premature removal from office. For instance, Pertinax was likely murdered by the Praetorian guard after failing to pay them in full. The famous last words of Septimius Severus to his sons, "be harmonious, enrich the soldiers, and scorn all other men", is a pretty overt example of the priorities of emperors with regards to the army by the end of the second century.

Hopefully someone else can chime in a bit more on the republic and the dominate. Needless to say none of this remained constant from the early days of the republic all the way through to the end of the Western Roman Empire.

I'd recommend Mark Hassall's "The Army" in Cambridge Ancient History Vol. 11 for a general overview, or Brian Campbell's The Roman Army, 31 BC - AD 337: A Sourcebook for more in-depth information drawn from primary sources.

As a rider, were they paid while on campaign? How were they paid - cash, vouchers, barter, or other? How was it that soldiers on campaign could financially support their families?

A slightly related question: I remember reading that roman soldiers could be payed in salt. Is there any truth to this?