It is not easy to explain package management (how to install software) in a few words. It is a difficult subject. The good news: learning it is rather fast and easy.
You don't have to download anything manually (like, for example, in Windows)
The software (packages) are offered from online repositories, servers where the packages are stored.
(or one can install from a CD or DVD, in case one has no online connection).
The user or admin installs them by a packagemanager.
There are several: apt-get and aptitude are commandline, synaptic and, i think, software-center, are graphical.
This way or that way you tell them: please install package xyz for me. The package-manager will check what other packages are needed (so called dependencies of a package), download the whole bunch, and install them.
I gave you the commands for apt-get, as that is the package-manager-frontent i know best.
Lots of people prefer aptitude.
The graphical ones have the advantage of being rather intuitive.
To make a long story short:
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sudo apt-get install gnome-desktop-environment
should install the whole gnome metapackage for you. It's size is ca (!) 3 or 3.5 Gigabytes.
If you later try to remove packages you might run into a well known dependency problems:
a package is installed as a dependency of gnome-desktop-environment, you want to remove it, and as that dependency of gnome is not fullfilled anymore, the package manager wants to remove all of gnome)
("aptitude keep all" should help with that, but it's been a while i have run into the problem.)
Once you are more comfortable with installing software you can decide how to go on (install gnome-core and the packages you need, or other solutions).
Perhaps you could install a small package first, to get used to it:
apt-get install synaptic
will install the graphical package-manager.
apt-get install feh
will install a small and easy picture-viewer.
Installing gnome will take some time (and doing new things one is usually nervous, or at least i am).
All as far i know. I hope this helps you a bit. The Debian wiki is a good start, though still overwhelming:
gnome is really way more heavy than lxde. I am not sure if you do yourself a favor with it, but you will see (i ran it on very low specs, it is not impossible)