First log in to your Blogger account, and from your Dashboard select "Layout."
Once in there, select the "Edit HTML" Tab.
Before you decide to upload your new template, it is highly recommended to backup your current one. To do that, just click "Download Full Template."
Click the Browse button, look for your template, and then click Upload.
If there are no Blogger warnings, you're done. If there are, it probably means that your widgets are going to be lost. If that's the case, be sure to keep a backup of each of them.
You may want to read this tutorial on how to upload your template without losing your widgets.