The Ubuntu software center has many packaged applications but does have the disadvantage that it cannot install .deb files. However there is another option.
Using GDebi to install packages
GDebi is a simple tool to install .deb files. It has a graphical user interface but can also be used in your terminal. It lets you install local deb packages resolving and installing its dependencies.. It automatically checks packages for their dependencies and will try to download them from the Ubuntu software repositories if possible. You may first need to install GDebi - simply install the gdebi package using one of the package managers listed above, or open a Terminal and type
sudo apt-get install gdebi
Once you have installed GDebi, use the File Browser to find the package you wish to install. Package files will look similar to this:
Double-click the package to open it with GDebi. If all dependencies have been met for the selected package, simply click the 'Install package' button to install it. GDebi will warn you if there are unmet dependencies, which means that there's dependencies that aren't resolved in the repositories that you're using - you will have to locate the required packages from some other source.