Editing the header – Size and elements

Hi there,
Being new to WP and CSS I cant figure out how to:
1) reduce the overall height of the header (Not sure of the pixel height, but about 60% of current)
2) remove the search bar from the header.

I see these are not dashboard options (that I can find) so looks like I must have to edit the code?
Any pointers on where to look, and what to change?

Here is a screen shot for visual reference
Thanks guys!

https://lh3.googleusercontent.com/-IOcytr6jIPw/USZ5uyK_lJI/AAAAAAAAFzs/DBogeoXAuwc/s1056/Home+-+Pilates+North.jpg