how to install an already downloaded package

If you have the downloaded .deb packages then just double click on it. If any messages shows out indicating that you dont have the permission to execute then do as follow -
press Alt+F2
type-
gksudo nautilus
browse to the package file, right click and go to permission tab

set owner as yourself and mark "allow executing as program". Now you can run it and follow the instructions.

If you have downloaded directly from "software centre" or "Add remove packages" , then you can find the packages in -

/var/cache/apt/archives/

in this case if you install the program again from software centre then the package wont be downloaded again, instead it would use the previously downloaded deb files found in the archive.

If the package is not deb...

.sh files-

first make it executable by command

chmod +x ./<name of the package>

then follow instructions above

.bin
most of the case works if you type

 sudo <package name>

.rpm
there is an application called alien (which you can install using Synaptic) that allows you (most of the time) to convert .rpm files to .deb. Read more about this process here -
https://help.ubuntu.com/community/RPM/AlienHowto

.tar.gz
The .tar.gz file extension indicates the file is a compressed set of files and folders (the compressed files you see in Windows usually have a .zip extension). If you see the .tar.gz, it could be compressed files that have a precompiled binary file, or it could be compressed files that have the source code allowing you to compile the application from source. In such case case
untar(unzip) the file and follow instructions given inside. This may help -
https://help.ubuntu.com/community/CompilingEasyHowTo