How can I implement this floating sidebar block? I'm going to implement a floating sidebar block that can contain user's selections. It is a kind of cart. Please check the image below.

If the use press 'Add to my favorite', then it should be contained in the sidebar. 
The floating sidebar block should slide up and down with buttons. Each item of it should be removed if the user press some kind of cross mark at the edge of item. 
After selection, the user can check all the items which have selected using 'View my favorites' button. 

What is the right solution to do this? 
I was thinking that I needed to use 'Views module'. But I can't imagine how to make this sidebar slided.
You can achieve it with HotBlocks module, Check out the screencast


Add, remove, and reorder nodes or blocks to a page without leaving or
reloading the page or using editors
Content added to hotblocks can be constrained to individual pages or
be made global to display on all pages that contain the hotblock
Can display multiple instances of the same block or node in multiple
regions
Can give end users the ability to add and remove blocks to pages
without exposing the administer blocks permission
Provides a means to filter which of those blocks are available to the
user for adding so every block in the system is not exposed
See an overview and administer all of your assigned hotblock content
grouped by region, url, or taxonomy on a single page
Allow users to add and remove content to a page without giving them
permission to edit that content
Advanced permissioning possible - allows you to control which roles
can assign/remove/reorder each type of content to every hotblock
individually if necessary
You can use your own custom icon set for the UI controls to customize
look and feel
If you don't like the term "hotblock" you can customize the
terminology exposed to the user to suit your purposes


and for floating use Floating block module.