Hi awesomeade, welcome to the Forum! First off, it will help if you put your X-Cart version number in your signature so that we can all assist you better.
Now, as far as moving the search box goes, you will want to open up head.tpl and cut this:
Code:
{if $usertype eq "C"}
{ include file="customer/search.tpl" }
{/if}
Then paste it in your customer/home.tpl template somewhere after this:
Code:
{include file="customer/categories.tpl"}
but before this:
Code:
{ include file="help.tpl" }
You will also want to edit the customer/search.tpl so that the advanced search text goes under the search box...that way it will fit in the column nicely under the categories. Good luck!