So how to switch from old template to new blogger template? Follow the steps below:
1. Login to you blogger account.
2. Click 'Edit HTML"
4. Download Full Template (for back up purposes in case you don't like the results)
5. Click the 'Design' button.
6. Click Template Designer.
From there you can choose from the new templates (the trusted ones) or design your own. Click 'apply to blog' when your done picking your choice. You can also adjust some things in there like background color, fonts attributes, width of sidebar and footer layout.
In terms of serps rankings, you may experience a temporary drop but as I said it's just temporary. Just keep on posting new entries and you'll be okay. Just keep all your entries clean. Minimized the use of copy pasted materials - yes, we all have a few of them - those who say they don't have, may raise their non-copy-pasted hand ^^. Again, I am only writing this from experience. Results of switching from old blogger template to new template may still vary. Switch at your own risk. I say "take the risk".