Once a book is loaned, the lender won't be able to read it until the loan period expires. That seems like an inconvenient limitation to impose considering the fact that we're talking about digital books here, but we assume Amazon has its reasons. Only certain books are lendable and publishers/rights holders have the final word on what titles qualify.
Loaning books is straightforward enough. Eligible books will have "Lending: Enabled" in the product description and the option should be clearly visible. Once you provide the borrower's name and email address, they have seven days to accept the loan. Borrowers can return the loaned book before the 14-day period expires by deleting it.