Removing a Search bar from header

What would a search bar html look like

This is very theme dependent. If your theme is from here, find their support forum page and pose this there.

If you simply want to hide or move the search bar:

For help with CSS, a live site link is required…if we cannot see the site, we cannot see the stylesheet(s), so we cannot suggest changes.

To discover what CSS is output by your theme, use a web inspection tool such as Firebug: http://getfirebug.com/ , Chrome Inspect Element: https://developers.google.com/chrome-developer-tools/ or Internet Explorer 9+ F12 Dev. Tools: http://msdn.microsoft.com/en-us/library/dd565627(v=vs.85).aspx#csstool

There are others.

When editing CSS, use a Child Theme
http://codex.wordpress.org/Child_Themes
Custom CSS Plugin, or Theme provided custom CSS option.
Edits to parent themes are lost on theme update.

Learn CSS: http://www.w3schools.com/css/