In the Little House books, Laura first sees Almanzo Wilder in the book By the Shores of Silver Lake in the chapter Moving Day. Laura was in awe of the team of horses that Almanzo and his brother Royal were driving, and Laura tells her father to look at the beautiful horses. While this is technically the first time she sees Almanzo, her eyes were all on the horses.
Laura is more aware of Almanzo during The Long Winter, because Almanzo played a key role when he and Cap Garland went to find wheat in order to save De Smet from starvation.
However, the courtship aspect of their relationship began during Little Town on the Prairie and one of their first significant interactions was when Laura and Almanzo exchanged name cards. Their courtship then continues through to the end of that book and throughout These Happy Golden Years, which culminated in their marriage at the end of the book.