Few details are reported about the trip itself, but it was no doubt arduous. Probably they followed a path similar to the one Ammon took to find them. They probably followed the correct river rather than the plausible error of the Limhite search party that had attempted to find Zarahemla. (See commentary accompanying Mosiah 8:8.)
Upon their arrival in Zarahemla, Limhi recognizes Mosiah’s right to rule, probably because (1) the Limhites were coming as strangers to a city with a greater population, (2) the historical fact that Limhi’s ancestors had been subject to Mosiah1, and (3) the recognition that Zarahemla was rescuing the Limhites.
Variant: The reading “joined Mosiah’s people,” was first introduced in the 1920 edition. Up to that date, the text had read “joined his people.” The clear intent is to reference the king of the land. The original “his” follows “arrived in the land of Zarahemla.” Because the land and city of Zarahemla were apparently named for the man Zarahemla who was the leader/ruler of the land prior to the Nephite arrival, the intent of the phrase is certainly to reference the king of the land. Of course, at this time the king was Mosiah, not Zarahemla. The change to Mosiah’s people makes the intent clear, but creates a situation where an anomalous construction was added to the text. All other designations of a people are “the people of… ,” not “someone’s people.”