Great question for anyone who has a newly published book and would like to hit the speaking circuit. I was once in the same boat and here is what I would suggest as the fastest and most effective method to getting your speaking engagements.
You must be active on social media. You should give away small tidbits of your book in videos and join FB groups related to your topic. There are millions of groups that you can join which will give you instant access to the people you need to know. When I ran for U.S. Congress, I joined the political groups of my party. Your book was written for someone at some stage of life, so find the groups associated with their interest.
I also hired someone to work for me 1 hour a day to make calls to decision makers of associations, conferences and trade shows. They would contact the organizer and send them the videos and one-sheets about me.
Use free speaking engagements to build your brand. Take lots of pictures, record videos and use these pictures in your promotional material. Cut and splice them. Be sure to wear different clothing to each speaking engagement, so you can have the appearance of different speeches in the beginning
It's always a great idea to have loads of books at any event to sell them after you speak.
If you have never spoken at an event before, consider joining meetup.com and find relevant meetups. First attend 1-2 meetups to understand their goals, theme, and topics that interest the participants - and then you can propose speaking there.
If you use slides, update your Slideshare profile and it builds your speaking portfolio. Next time, use this Slideshare profile to send proposals to other events - city level, and then regional and others.
Identify people who are speaking at the events where you want to speak. Engage with them (social, emails, or in person if they are in same city), and exchange value. They should be happy to propose your name as a speaker in future events.
Important: "Value" is the keyword. Good luck for your book!
The easy way if to bridge your book to a topic related to existing speaker networks or large conferences.
Let's say your book is about writing better.
Bridge this into how to write better blog posts + then speak at WordCamps talking about...
1) Technologies assisting people writing better - plugins + services.
2) Techniques for writing better (your book + consulting).
BTW, keep in mind the difference between Rich Authors + Poor Authors is Rich Authors have deep back ends. They understand a book is just a lead generator.
The real money is what books lead to in the form of consulting or other services.
To make $1000/month selling a $10 Amazon Kindle book, you'll have to sell 142 books/month.
To make the same $1000/month consulting, you only have to make one consulting sale, where someone pays continuity for $1000/month in services.
Math always favors high ticket continuity sales, driven by book sales... Never living off book sales...
Trying to live off book sales with leave you with an angry spouse + skinny kids.
You can search for Associations that work within your topic of the book, you can get booked on podcasts, or even get booked for a TEDx talk.
The best way to get booked is:
1) what is your message to the world
2) who needs to hear this
3) where do they hang out
Answer these questions and you are on the path to getting booked. I wrote an entire guide on how to get booked to speak. Bit.ly/GetBookedToSpeak