Where do these grounding wires go?
simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. Various "ground" symbols.

In most circuits there is a common rail which is used as a reference for all other points in the circuit. One of the most common examples is the automobile / car electrical systems which use the chassis as the return path to the battery negative. Most circuits use the power supply negative as the common rail but many don't (and cars used to use positive earth many years ago).

Using a symbol for ground makes schematics more readable as it eliminates many wires. 


The signal ground symbol is commonly used in electronic schematics.
The 'earth' symbol is used for a real earth connection on an electrical power distribution diagram but is often seen in auto electrical schematics and electronics circuits to signify a connection to electrical ground.
The 'chassis' symbol will appear in electronic schematics to indicate connection to the metal frame or chassis of the device.


In an isolated system - your mobile phone, for example - the "ground" is isolated from everything else until you plug it into a charger.


  Does this mean that the circuit is self-grounding?


No. It just means a common "ground" or reference rail.