Open up Finder
I think it defaults to your home folder, but if it doesn't navigate to your home folder using the SideBar
Within here, make a new folder 'Downloads'
Drag that folder over to the Sidebar for ease of access
Once it is there, navigate to the desktop, highlight the files, and drag them to the download folder.
Now, open up your browser, and press Apple+,
Find in there what you need to change your download location. Change it to your newly created download folder.
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By Taskbar, I assume you mean the Dock (gots to get the names right )
Ok, you don't want your Dock cluttered, I can appreciate that. Here are some tips
Hit Apple+W to close a window (95% of the time, this will not quit the application, there are exceptions)
Apple+H hides the window, but leaves it as it was
Apple+Q quits an application
Apple+M minimizes an application to the dock
If you have applications on your Dock that you don't want, simply drag them up and off the dock, they will disappear in a puff of smoke.
Bear in mind that your Dock has 2 parts. Left and Right. There is a line that divides the two parts, the right side is reserved for the Trash Can, and minimized windows. The Left side is where you put applications a la Quick Launch. When you have an application open, a little triangle appears underneath the icon on the Dock letting you know that it is open. Any apps that you have open, but not permenantly placed in the Dock will appear to the immediate right of your far-right-most permenant application.
A B C D | Trash
^This is your Dock, A,B,C and D are your 'permenant' applications and | is your divider
A B C D e f g | h Trash
^Here is your dock with 3 non-permenant open applications, 1 minimized window and the permenant apps