There is no different way to write it, you can use:

J’ai appris à lire à Sarah

or, to avoid two consecutive à xx:

Sarah, je lui ai appris à lire

It is not incorrect but j’ai appris à Sarah à lire sounds less common, probably because it breaks the compound apprendre à lire.

The word “apprendre” means also to acquire a habit, for example, “il connaît les règles, mais il refuse d’apprendre à les suivre”, it doesn’t mean that he doesn’t know rules.