pacman -S extra/gnome installs a lot of things, including Xord and GDM.
extra/gnome is a group of packages which you can select or deselect in
pacman. But for a typical gnome install you're very likely to want all of them.
From there you can simply enable GDM to run on boot with:
systemctl enable gdm.service
The you can either reboot or use:
systemctl start gdm.service
To start the display manager right there.
Get into the display from tty
To start gnome from the command line, you want the GDM service to be disabled.
systemctl disable gdm.service
And you need two files in your home directory
.xinitrc. To make things simpler it is wise to use a
.xsession that calls
.xinitrc. For example
if test -r "$HOME/.xinitrc"
And then you can place whatever you need in
# Sometimes D-BUS stuff is placed here by packages, pick it up
if test -d /etc/X11/xinit/xinitrc.d
for f in /etc/X11/xinit/xinitrc.d/*
[ -x "$f" ] && source "$f"
# random config
# get into gnome
Now, this is important, both files must be executable.
chmod 755 .xsession .xinitrc
And you can perform
startx from the tty to start Xorg and then Gnome.
Arch has several drivers available from the main repositories.
extra/nvidia has the latest ones (latest ones in the official repos, AUR will have slightly never ones).
extra/nvidia-304xx are the ones for older cards.
I'm not following NVIDIA's name conventions, you will need to go through the arch wiki and nouveau conventions to find which one has a chance to work.
But really, something of the lines of:
lspci -k | grep VGA
Will also give you a better idea of the name of your card.
Xorg is a display server, it deals with creating the display (or several displays).
GDM is a display manger, it deals with authentication and communication between the display server and the window manager.
Gnome is a window manager (actually it is other things as well but for our purposes it fill the window manager application stack), it provides the user with tools to interact with the display and applications with the API for windows (through GTK).