Can somebody recommend techniques to make a search input look like:

I get the button part, that's easy. It's the input box that I don't know where to start.

This is just a recommendation but I would recommend that you not alter the default install files.  The breakdown on why is fairly simple, if you alter the default files the first time you upgrade you will lose all of your work and if you are running multiple portals and would like a different look for each, you cannot do this by altering the default files.  The way I have worked with this in the past, and it may not be the best so feel free to correct me, is to take the default files and create a new folder for each set of files with a different name.  Paste the original files into the new folder and you should be able to use it in you skins.  In the case of the search files, I created a folder under /Admin titled Search2.  The folder structure ended up being /Admin/Search2, then I created a new file under /Admin/Skins titled Search2.ascx.  I then copied each of the files from the /Admin/Search folder to the /Admin/Search2 folder.  I then modified the file Search2.ascx to fit as I wanted it to.  If you don't change any of the vb code and just change the look and feel of Search2.ascx then it will function as a regular search with a different look.  I build my skins in ascx, so I just add the appropriate changes in the file, if you build html skins it might be a bit more tricky, I would have to check, but it shouldn't be too difficult. 

I may have missed a few steps so you can feel free to email me or post here and I can answer questions, if you have them.  The added advantage of this is each time you upgrade, you keep the custom look.  The disadvantage is that you will have to upgrade the custom skin object seperately.  We have been through a half dozen upgrades and haven't needed to fix any problems yet.  You can also work this out with some of the other modules, I did it with the Links module, but you may want to be careful doing this with some of the more complicated modules.  These are, of course, just recommendations but it may make your life easy.