Building complicated home pages

SO I am trying to make the jump from Joomla to WordPress, and there are definitely a few hitches. Theres really only one thing I can’t figure out.

If I want to build a complicated home page (ie a page with many elements) how do I make plugins and widgets show up on JUST that one page?

Heres an example. Lets say I wanted to build this: DESIGN IDEA, NOT MINE

I understand that I’d choose my template page that’d be specifically coded for the home page. Got that. But lets say I wanted build that top image as a slider, and to include that map at the bottom. How do I do that? I know I can get a slider plugin and that I can use shortcodes to include it in a static page, but is the whole page built like that? With shortcodes and html blocks? With Joomla I’d have modules and custom HTML blocks assigned to named spots in the template and then assigned to specific pages. I havent’ been able to figure out this out for WordPress yet…

If anyone has a link they can send over for stuff like this, it’d be much appreciated.