First step is to login at
Blogger. If you are using old classic Blogger, your Blogger Dashboard will be looking something like this.

Click
template and click
customize design.
Click
upgrade you template, and Blogger will transfer your classic Blogger template into new Blogger layout. Blogger will automatically save your old template and you will always have the option to revert back to classic Blogger :).

Now, Blogger will ask you to choose any of the default Blogger layout. Choose any layout and you will be given the option to choose any customised Blogger layout later ;). For example, I choose the first Blogger layout which is Minima.

Once you do that, you are now have successfully transfer your Blogger account into new Blogger layout :D.
Now, the explanation after this will demonstrate the steps to upload any customised Blogger layout to your blog.
Click
edit html. 
Click
browse. Find the location of any Blogger layout that you have saved in your computer. The file should have the extension of
.xml. For example
Blogger.xml . If the file does not have the extension of
.xml, the layout will not be accepted by Blogger.
Once you have found the file, click
upload.

Now, you should have something like in the picture below. Blogger will ask you whether you would like to like to delete widgets.
What are widgets? Blogger widgets are mini application that helps you to add anything to your blog. You do not necessarily need to know any programming language to edit widgets. For example, you can easily add links, shoutbox, RSS feeds, third-party javascript using widgets without having to modify the whole layout manually.

Since this is the first time you are using new Blogger layout, your current widgets will not contained any information. Thus, click confirm and save.
You will be directed to page elements under template tab once you saved your new Blogger layout.

This is the example of page elements of my template,
Ladybug. Do you know that you can drag-and-drop the page elements in page element editor? For example, you can easily put Labels on top of About Me. It is a cool feature in new Blogger layout B-).