Customize, Choose Forms & Alerts (Base CSS) and Close Icon (Miscellaneous) if you want to use jquery validation and display alerts. You may still need to CSS !important override some input styling.
e.g.
#cse-search-box, .searchbox {
padding: 0 !important;
border: 0 !important;
font-size: 100% !important;
font: inherit !important;
height: 14px !important;
webkit-border-radius: 0px !important;
-moz-border-radius: 0px !important;
border-radius: 0px !important;
border: none !important;
outline: none !important;
-webkit-box-shadow: none !important;
-moz-box-shadow: none !important;
box-shadow: none !important;
line-height: inherit !important;