How do I make search box appear in front of logo image?

I have finally worked out how to put in a logo image at the top of the screen... but now the search box disappears behind it. What am I doing wrong?

I also would like to have a my own search button connected to the search field (that you can click). Where should I upload this and should I change any code(where/what)?

I know that there are many threads already dealing with these matters... but I have very little experience in code and basically don't understand the short replies given. Can somebody help me?