This method am about to show is very easy and does not require much work.
Follow the steps below.
First you will have to go to the Facebook developers web page, there you can get everything you need to perform this.
Now on the Facebook developers page you will be given different options to choose your preferred like button either recommend or like.
Now click on get code then a pop up window will pop including the like button code just copy it.
Sign up to your blogger blog and then select the blog you want to work on.
Now on the blog dashboard scroll down to your template tab click it then edit template.
Then click on the html code and then cltr+F search for this code below
The code you copied from the Facebook developers page paste it below the code above. and then save your template that is all you need.
When doing this you will have to do some editing to the code being achieved from the Facebook developers page just follow the arrangement below.
Paste your code here