This part will focus on the USB-C connector itself. Check out Part 1 for an overview of all the USB3.1 specs.

The USB Type-C connector is slightly larger than the micro-B connector. It has 24 pins in a radially symmetric pinout, making its orientation reversible. Unlike previous versions of the USB connectors, there is no physical distinction in the plug depending on the functionality supported by the port or plug. USB-C does it all.

The Type-C Spec is part of the USB3.1 Spec, as explained in Part 1. You can download the full USB3.1 specification from usb.org. Follow along with the USB Type-C Specification Release 1.2 in the USB Type-C folder.

Pinout

Taking a quick look at the pinout, the radial symmetry is obvious. The GND pins are always on the outside, and the VBUS pins are always four in from the outside. GND, VBUS, DP, DM, and SSTX/SSRX are all familiar from the USB3.0 spec. The new pins are CC, VCONN, and SBU.

Section 3.2.3 of the USB Type-C Spec (page 55) lists the pinout in more detail, but here's a summary.

VBUS - provides power to the sink
DP/DM - USB2.0 communication, up to High-Speed USB (480 Mbps)
SSTX1/2, SSRX1/2 - SuperSpeed transmit, differential pairs, usually twisted pairs in the cable
CC - Configuration Channel used to configure the connection and send Power Delivery messages
VCONN - Connector power to power active cables and accessories
SBU - Sideband Use, basically extra wires used in Alternate Modes

Traps for the Unsuspecting

The SuperSpeed Tx and Rx lines swap in the cable. So do the SBU wires. That means that SSTX1 on one side is connected to SSRX1 on the other side. Similarly, SBU1 is connected to SBU2 on the other side. You cannot use the mux to fix this. I speak from personal experience.
The differential pairs will have a 90 Ohm differential impedance. If you are using an alternate mode, make sure it can handle 90 Ohm +/- 5 Ohm (section 3.7.1)
Cables can be electronically marked. This means there is a microcontroller inside one of the plugs, connected to the CC line. It is responsible for reporting the capabilities of the cable. "All USB Full-Featured Type-C cables shall be electronically marked." (section 4.9). Cables that only support USB2.0 do not need to be marked.
Be careful powering anything off of VBUS. With USB Power Delivery 2.0, VBUS can go up to 20V. Make sure this doesn't violate voltage ratings in your circuits. Benson Leung has had a few incidents in his famous Amazon reviews. Consider making anything connected to VBUS or CC over-Volt tolerant.
Also be careful powering anything from VCONN. You might not have it. Or you might have to provide it. Check in with section 4.4.3 of the spec.

Muxes

To support the reversible pinout, and make things easier for the user, each USB receptacle is required to have "the functional equivalent of a switch in both the host and device to appropriately route the SuperSpeed TX and RX signal pairs to the connected path through the cable." (section 4.5.1.1) The USB spec leaves the implementation up to the designer. For USB2.0, you can just short both possible positions together. For the SuperSpeed pairs, this usually means you need a mux.

Figuring out which way the cable is connected is done through the use of the CC line. This wire is always in the same location on the plug, and it can only be connected to one of two pins in the receptacle. The location opposite CC in the plug is VCONN. This is why the plug has CC and VCONN, but the receptacle has CC1 and CC2.

Using the CC line

The Configuration Channel is used to determine plug orientation, communication device roles, power capabilities, and send Power Delivery messages. Section 4.5 of the spec describes the details about this line and its uses.

To communicate device roles, pull-up (Rp) and pull-down (Rd) resistors are used. In reality, these will likely be current sources and sinks. In general, devices that once had a Type-A port will use the pull-up, and devices that once had a Type-B port will use the pull-down. In the below example, the source looks for a drop in the voltage on either CC1 or CC2. The pin that drops with an Rd pull-down is connected to the CC line. When it sees that, it can then provide power to VCONN and VBUS.

Meanwhile, the sink is monitoring for either CC1 or CC2 going higher in voltage. Then it can activate a pull-up on the other pin to read the value of Ra (pull-down for accessory).

Type-C Current

Even without supporting USB Power Delivery, it is possible to get as much as 15W through the USB connector. VBUS is still limited to 5 Volts, but the current can be as high as 3 Amps. This is done with analog signaling of voltages on the CC line. Essentially, the source changes its value of the Rp pull-up resistor to set the voltage of the CC line within certain ranges. Section 4.6.2.1 describes the details, and section 4.11 has the parameters.

USB2.0 Designs on Type-C

Supporting Type-C from an existing USB2.0 design is straightforward and cheap (except for the connector). Basically you tie the DP pins together, tie the DM pins together, and add one pull-down resistor to each CC pin. This new Type-C device will identify as a data and power sink, use the default USB2.0 power of 500 mA, and work in either orientation of the plug.

Type-C Connector Designs

In the last year alone, many new designs of USB-C connectors have come onto the market. Most of the major players have a good line-up. Here's a few parameters to consider, beyond the usual.

USB2.0 vs USB3.0 vs USB3.1 - Usually Type-C connectors are rated for a max data rate. USB3.1 supports up to 10 Gbps, USB3.0 would be 5 Gbps, and USB2.0 is 480 Mbps on the DP/DM pins. USB2.0 might not have as much shielding.
Right-angle vs Vertical Mount - Fairly self-explanatory. Be sure to have a plan to mechanically support the vertical mount connector.
Dual-SMT or Hybrid - Some connectors have two rows of 12 SMT pads each. The hybrid connectors have a outer row of SMT pads and an inner row of thru-hole pins. Beware that usually the thru-hole pins are designed for 0.6-1.0 mm thick PCBs.
Current and Voltage Rating - Gone are the days you can rely on USB connectors supporting the current and voltage you expect. If you need more than 3.0 Amps or 5.0 Volts, take a close look at the current and voltage ratings.

More Info

Here's a few links to check out with more detail.

If you want to experiment with Type-C at home, you can buy an Fairchild FUSB302B Power Delivery PHY breakout board from my Tindie store and download the library I put together from GitHub. Just add an Arduino and you're good to go.

Part 3 will take a closer look at USB Power Delivery and the BMC signaling uses on the CC line to set up features like higher voltages on VBUS and Alternate Modes.