To request books be sent to you:
Books are checked out to you for 8 weeks, and can be renewed once.
If you can't wait the 5 days or so for a book to arrive via UPS, try these alternate solutions:
If one chapter looks particularly promising, requesting just that chapter is faster since the chapter will be scanned and sent to you. Chapters are sometimes listed in the book's catalog record, or on Amazon or Google Books.
If your book is not a textbook, and is more focused on a broad public audience instead of experts, the public library is more likely to have it.