The download location is controlled by the application and its settings.
You did not say what application, but go to the settings and change the
default location. For example in Chrome go to Settings and click the
Advanced settings section at the bottom. Then scroll down to where it says
Downloads. In FF go to Edit, Preferences, General tab, Downloads: Save to
...

You will have to find the settings for other applications such as
Bittorrent clients etc. and change each. The reason why this is not done
globally is because you likely want Music in a different place from Deb
files, for example.

I can change the setting. I do have Firefox. Do I
need to do this every timeI change from music to download to pictures, etc.?
Windows, it just asks where you want to save it and it goes there. My next
question is where are the files that I downloaded? Is there a search function?

It's possible to set Firefox ( or any browser ) to ask each time, just
as it's possible to set any browser in Windows to dump all downloads
into a specific folder. Nothing to do with the OS, it's a browser
setting thing

Ubuntu has very good searching capability but the method varies
according to which version of Ubuntu you are using. If you have the
Unity interface with Launcher and Dash Home then click on Dash Home
and just type the name of the file / folder you want to find. In other
version open whatever file manager you have and click on the 'Find'
icon to begin your search. Every one has its own quirks and needs a
little getting used to, but all searching is similarly something of an
art so it's worth getting into the habit of saving things where you
know where they are

I just looked and all my downloads already go to downloads. The trouble is that
I cannot find the files in downloads. Is there a good file system?

If everything is set to go to 'Downloads' and the ones you are looking
for aren't there then it's possible that the download didn't complete
so try getting them again.

Yes there are file system viewers and again exact information depends
on what version of Ubuntu you are using. Ubuntu uses Nautilus whereas
Kubuntu used Dolphin but there are multiple others you can install
with each having its strengths and weaknesses. Looking back I see you
had Ubuntu 11.10 and that was the second release that had the Unity
desktop - i.e. with the launcher bar on the left hand edge of the
screen. If you are still using that then the second icon down on the
left should be 'Home' and clicking that starts the Nautilus file
manager where you can access anywhere on the HD.

If open the Downloads in FF under Tools in the menu it will take you to the
downloads page and you can Right Click on individual files in the list and
either Open or Open Containing Folder. If you get in the habit of saving
them to the same location then you can make a shortcut on your desktop,
panel or launcher, depending on the desktop environment that you are using.

I save various kinds of files in the appropriate place instead of one.
Music goes in a Music folder, Pictures go in Pictures, PDFs go in
Documents, for example. This takes a bit more work as you save, but it
makes it easy to find things on the back end. It all depends on how you
work.

For me I just let it all go to the Downloads folder, then I have other
folders in there and manually move them to where wanted. For instance
I download applications I want to test for ham radio, so I store them
in a folder so named right in Downloads, but I also download some PDF
files of documentation for some of those same apps and keep them in
a separate folder under Documents named PDF and under that folder
subject name. Everyone has there own way of doing things but keeping
all downloads in the same place allows me to know where end up and I
then sort it out.

That works, too. Some people do not like using the file manager to move
files, though. Everything depends on your comfort level.