The initial Session dialog consists of several consecutive pages:

Open Session Page

On this page, you can open an existing session. You can also open any snapshot of a particular session by clicking on the arrow next to the session name to display all snapshots, and then selecting one. If your session is not displayed in the Recent Sessions list, the Other Sessions button will bring up a file selection dialog to navigate your hard drive.
Alternatively, you can opt to create a New Session.

New Session page

Here you can type in the name of a session, select a folder to save in, and optionally use an existing template.

Under Advanced Options, you can select whether you wish to create a Master Bus, or a Control Bus, and how many channels you wish either to have. You can also decide whether you want Ardour to automatically connect all inputs to the physical ports of your hardware. Ardour will do so sequentially and in round-robin fashion, connecting the first track's input to the first input of your hardware and so on. When Ardour has used all available hardware inputs, it will begin again with the first physical input. You can limit the number of channels on your physical hardware that Ardour uses.

By default Ardour will connect all tracks and busses to the Master Bus if there is one. However you can also tell it to automatically connect each output to the physical outputs of your interface or sound card, and limit the number of physical outputs used, as above.

Audio/MIDI Setup

This page is not displayed if JACK is already running when you start Ardour. It provides a simple interface to configure JACK, which will then be started by Ardour. For more control and options regarding JACK, it is recommended that you start JACK before using Ardour, via a JACK control application such as QJackCtl (sometimes called "Jack Control"), JackPilot, etc.

Audio System

Currently, the only option here is JACK. In the future, native hardware access may be supported.

Driver

On Mac OS X this will typically be CoreAudio. On Linux usually this will be either FFADO or ALSA, depending on whether or not you are utilizing a firewire device. Advanced users on all platforms may also use NetJack which provides network audio I/O.

Device

The selector should show all availiable interfaces provided by the driver above and which are capable of duplex operation.

If you are using an Intel Mac running OS X and the builtin audio interface, you must first merge its separate input and output devices into a single "aggregate device" before Ardour will be able to use it.

Sample Rate

The selector will allow you to select from any sample rate supported by the device selected above it.

Buffer Size

You can adjust the size of the buffer used by your audio interface to allow for either lower latency, or lower CPU usage and higher latency.

Input/Output Channels

Here you can specify the number of hardware channels to use. The default is all available channels.

Hardware Input/Output Latency

Specify the hardware delay in samples for precise latency compensation.

Calibrate

This button guides you through a semi-automated process to obtain precise hardware latency measurements for the above option.

MIDI System

Select the MIDI driver to use. On Mac OS X, this will be CoreMIDI. On Linux, you can change between two legacy ALSA drivers or the (preferred) new JACK+ALSA implementation.