On the TinyLily Mini, the numbers shown correspond to the Arduino "pin numbers", such as for the digitalWrite function. So 0 as marked on the TinyLily Mini is accessed as pin number 0 in the Arduino IDE. The ones that have the A prefix are analog pins. In total, digital pins 0, 1, 2, 3 are supported, and analog (or digital) pins A0, A1, A4 and A5 are supported. There are also some alternate functions on the pins (the same as an Arduino Uno), so A4 and A5 can also be used as I2C pins, and pins 0 and 1 are connected up to the USB programmer.
Because 0 and 1 are connected to the USB programmer, you can't use this pins at the same time as when the USB is plugged in (which is why it might look like they are not working to some people).
The + and - pins are power and ground. There are two sets of these, and they are connected together. The reason for this is that you can have a battery hooked up to one pair, then the other pair can be used to provide power out to any peripherals you have.
The 6 pins in the middle (that aren't soldered to anything) are for an in-circuit programming connection. This lets you program the microcontroller initially with the Arduino IDE, and a 6-pin connector can be soldered in to allow ICSP programming and debugging using an external debugger, but most Arduino users will never use this. If you look at the schematic, the ICSP connector used the SPI pins on the processor, so if you absolutely need some additional I/O points, you can grab a few more signals off of this.
Thanks,
Ken
TinyCircuits