Hi,
The simplest way is to use the search shortcode. Adjustments are probably still required – as each menu works very differently. Margins, paddings, heights, alignments depend on the menu layout.
Usually, negative/positive left and top margins are sufficient to adjust the search container to the menu. I suggest a custom CSS like this:
.asp_m {
margin-top: -10px !important;
margin-left: 0px !important;
}This is only a sample code. The values have to be experimented with. If the search alignment is higher than the other menu elements, then try positive top margin, otherwise negative. Same for the side margins. But again, this highly depends on the exact layout, some additional adjustments might be required.