They do not receive payment, quite the opposite. Part of being a Solmanic Knight means you give some of your income to the Solamnic Knight institution to support the training, feeding, lodging, and upkeep of the Solmanic Knight empire.
Knights of the Crown are expected to give 10% of their wealth (or income) to the official coffers.
Knights of the Sword and Rose are expected to give 100% of wealth except those required for upkeep for lands or property (castles, fortresses).
Before Gunthar's modification of the Measure, most knights (or all) were historically royalty from Solamnia, and therefore had lands and other resources at their disposal. Presumably they may impose a tax on the people living and working their lands in return for their protection. It is stated that before the Catacylsm, there were only 69 total Solamnic Knights, all others were
conscripted army, footmen, usually local guards, militia and mercenaries, acting under the commands of a Knight - dragonlance.wiki
There were even fewer after the Catacylsm.
When Laurana became the popular Golden General, there was a huge surge in enlistment in the knighthood. Gunthar Uth Wistan remarked that their coffers were 'full' for the first time in years. This is probably on account of receiving the income of new squires and knights of the crown who had enlisted, in addition to donations from cities (such as Palanthas). The knights were now seen as favorable for the first time in 300 years.
During several centuries, the Knighthood only accepted squires coming from noble families located in Solamnia...In more recent times, squires can enter the order so long as they are honorable. - dragonlance.wiki
An example of this would be Tanin and Sturm Majere, who were not from Solamnia (or royalty), but were both accepted into the Knights of Solamnia.
Those knights who didn't come from royalty probably had very little, but as knights they had no reason to seek riches. They were provided with clothing, weapons, food, lodging, and mounts (circumstances providing). As knights they lived frugal lives.
The oath is
Est Sularis Oth Mithas,
My Honor is my Life. The Measure is a set of rules by which a knight is expected to behave in any number of situations. Unless a knight acts in a dishonorable way, he is a member for life. If he is found to be dishonorable before a council, he may be disbanded from the knighthood (such as Lord Soth), or lowered in rank.