Never limit your choices when it comes to traveling. There are a multitude of ways to book your trip. I could literally write 14 pages on how to research and book a trip, but no one has the time or attention span to read a post that long, so I will spread out the info through multiple posts.
The key thing to know, is that there is not one right way to book, but many ways. It depends on your needs. Are you restricted on time? Expense? Preference? Flexibility? Do you like extra perks? Are you a fan of loyalty programs? These are things that need to be considered before booking.
Service providers websites, third-party sites, online sales and coupons, search engines, and travel blogs are all tools you can utilize in your travel planning toolbox. But just remember, like a screw driver, one size does not fit all.