How do I manage applications on startup in GNOME 3?

From terminal or Alt+F2 dialog run: gnome-session-properties.

For newer ( 3.14+ ) versions of Gnome just use the Tweak Tool from the applications menu.

None of the other solutions worked for me in GNOME 3.14 on Ubuntu GNOME 14.10. What finally worked, was creating .desktop files by hand.

First, create the ~/.config/autostart/ folder, if it doesn't exist.

Then, create a ~/.config/autostart/my-app-to-startup.desktop file for each program you want to start on login.

For example, here's what my ~/.config/autostart/pidgin.desktop file looks like:

[Desktop Entry]
Type=Application
Exec=pidgin
Hidden=false
X-GNOME-Autostart-enabled=true
Name=pidgin
Comment=instant messenging client

Here is the specification for the keys you can place in those .desktop files. This puts some context to that specification as to how it applies to startup applications as well as some exceptions to those rules. Credit for this solution goes to this Linux and Friends site.

As rossouwap's answer is not working any more on Gnome 3.14+ now you should type Alt + F2 then run gnome-tweak-tool on the dialog and then look for the tab Startup Applications.

EDIT
I assume you have Gnome Tweak Tool installed. If not, run this on the console:
sudo apt-get install gnome-tweak-tool