The best thing to do if you want to install an app in ubuntu is to use
synaptic package manager untill you are very familiar with it. Otherwise
look got .deb files that are compatible with ubuntu.

If the software that you have downloaded is something that you cannot find
in synaptic, then u will have to find out if its compiled, or just source
code.

if its compiled, you can execute it. If its sourcecode, then you need to
compile it, and then execute it.

Synaptic is the best way to install programs and should all ways check there
first. If you have your extra repositories enable. You'll even get more
programs to install. If you know the deb package you want to install. The easy
way is to open up the terminal and type in
sudo aptitude install (name of program)
Here is several link on you question too.

http://monkeyblog.org/ubuntu/installing/
http://psychocats.net/ubuntu/index

Give me an example of what you are downloading and from where?

I'll try to play a video clip using firefox and I'll be told that to do it I'll
need Adobe Flash Player to run it. I go to the Adobe site to download it.
After I've downloaded it I decompress it and read the read me file. The read me
file tells me to go to the install directory and run the install command. I
have tried to do this, but haven't been able to. I think my problem is getting
myself maneuvered into the right directory to run the command, but I'm not sure.
What is the best way to move around in directories and properly execute the
commands?

The latest tarball download of the flashplayer plugin at

http://labs.adobe.com/downloads/flashplayer9.html

has a shell script installer in the extracted directory named
"flashplayer-installer". It is marked as executable so you can run it from
a terminal as follows:

cd ~/download/install_flash_player_9_linux
./flashplayer-installer

Running the installer as above will install it in your home directory which
is OK. To install as root for multi-user use:

sudo ./flashplayer-installer

For firefox, all you need is the flashplayer plugin: "libflashplayer.so".
So you can just manually copy it to "/usr/lib/firefox/plugins".

sudo cp libflashplayer.so /usr/lib/firefox/plugins

Flash player 9 is in synaptic..... You do not need to install from source. It
may break the package and then you need to correct it if it does.

you can open up the terminal and just type in

sudo aptitude install flashplayer

that would be it and wil be done installing flashplayer 9

Actually it is not in the Feisty repo's

However, you can download the RPM version from adobe.com and then
convert it to a DEB using "alien".

If you really can do this...prove it....
so far all I have seen is tutorials on how to do so with an x86 box and I am
running an AMD64 box.

For flash player9 for AMD that is running the 64 bit kernel that is different
and me bad.
https://help.ubuntu.com/community/AMD64/FirefoxAndPlugins?action=show&redirect=F\
irefoxAMD64FlashJava
There is more work to be done for AMD running 64 bit kernel. It was wrong of me
to assume so. Yet, the link would get in working about 15 minutes,

I have been using Automatix. A lot of people says is no good but for me has
worked up to now!!!

www.getautomatix.com/.../automatix2_1.1-4.7\
-7.04feisty_i386.deb

I hope it help.

All codecs are in and also a lot od apps.

Come to think of it...I think the bugginess miight have been around the time
I tried to do something similar (perhaps the same?) as what that link tells
me to do...because I wanted to see flash on myspace and utube.

If you enable the extra repos it will be there. Yet, not for AMD users running
64 bit Kernel

firefox says 'extra plugin has to be installed to view the video'.
Click on the space where the flash applet appears. firefox automatically
searches for the missing plugin and installs it on ur computer. u dont even
have to restart firefox!