The sidebars will go away.    Before they do, copy the content you need from them to somewhere else in the site.

If you have a custom theme, save its tpl definition for later reference.  Save in a file on your computer.

In appearance, set the layout to one of the Resp_ ones.  You may need to set the filter settings on the layouts.

In appearance, set the theme to one of the responsive ones. You may need to scroll down and click "See responsive Themes"
Warning: It will look terrible until the next step. 

Use Administration/Configure Site/Site Preferences.    Scroll to the bottom and set HTML version to HTML5.

In appearance/backgrounds, "Reset to Default" anything that may have been set.  Remember the settings in case you want to explore readding them after all else is working.

Find the menus such as in the header and footer, make sure they work. Configure them if needed.

Consider using Fine Tune Layour to adjust what is shown in the header or footer.

From the advanced admin screen regenerate thumbnails.   Now that the site is in HTML5 these may differ.

Find older picture albums.   Insert a new one.   Use add pictures and in the dialog you can import from the prior block.

TBD