Solomon first met Dodger when two thugs attempted to beat up Solomon (they didn't need a reason; this is Victorian England), and the tosher saved him. It seems that Dodger meets a lot of people this way. In those days Dodger had been quite unpredictable; if he had been feeling differently, he would probably have been the one to kick the old man. But as it was, he took him home and the two became firm friends. They soon came to an agreement; Solomon would cook meals, while Dodger would help the man in various small ways. His protection was very helpful, as his hard-earned reputation ensured that even the toughest rogue thought twice before coming near either of them.
Solomon ended up in London as a refugee from eastern European pogroms. His flight -- across Europe and the world -- from the Cossacks brought him into contact with numerous cultures, and many and varied people from those cultures. At one point Solomon hid out with a young man name Karl, who had interesting ideas about workers possessing the means of production.
As a result of his extensive travels, Solomon becomes quite cosmopolitan, wise in the ways of the world. When Dodger -- who initially is portrayed as precisely the *opposite* of cosmopolitan -- begins to make acquaintances in upperclass London social circles, it is Solomon who acts as an etiquette guide. By combining his understanding of how to fit in with people with his myriad relationships in the London Jewish community of small business owners, Solomon helps Dodger insinuate himself into high society, and to make himself ever more attractive to the mysterious rescued princess.
It is not hard to jump to conclusions when an elderly Jewish man rents spaces to a boy called Dodger in a Dickensian-themed novel. Indeed, the physical description of Solomon matches Fagin (of Oliver Twist) quite well, or at least a Fagin who has stopped committing crime and has completely reformed.
Interestingly, Dickens based Fagin off Isaac 'Ikey' Solomon, a thief who owned a Jeweller's shop. See here for more information.