Negative voltages in the real world?
There are basically three ways to do this.  One way is two independent, isolated power supplies.  Say, two batteries or two bench supplies.  Connect them in series, + to -.  The connection between the supplies becomes 'zero', and then one supply gives you + and the other gives you -.  The second way is to use a bipolar power supply.  This is a power supply that is specifically designed to output equal and opposite outputs around ground.  It is basically a single-output power supply with an additional output that is 'mirrored' over the ground connection.  In this case, the supplies do not need to be isolated, but you will need to use complementary parts (NPN vs. PNP or NMOS vs PMOS pass transistors, 7805 vs 7905 regulators, etc).  The third method is to use a single supply with double the voltage and then synthesize a virtual ground halfway in between.  See http://tangentsoft.net/elec/vgrounds.html for many useful details on how to build virtual grounds.  

Edit: It is also possible to generate a negative supply from a positive supply with some sort of switching DC to DC converter.  An inverter would be the simplest, using either a standard inverter topology with an inductor or a flying capacitor charge pump.  An isolated flyback converter would also work.  These can be procured as complete modules from various suppliers.  A charge pump may not provide very much current, so watch out if you decide to use one.  Switching supplies can also create quite a bit of switching noise, both directly coupled into the output and also radiated from the high current switching components.  This may require filtering and careful design to prevent interference.  

Also, please don't rotate your voltage sources upside down; it makes the schematic very confusing.  I would recommend moving V2 and V3 next to V1, one above and one below the ground wire, and both with the positive side up.  Then connect them over to the amplifier with long wires.  This makes the required power supply configuration very obvious.