Begin building your own DC to AC inverter by assembling the oscillators, then attach the transistors to the heat sinks using an isolation kit. Attach the heat sink and power transformer to a thick metal enclosure. Connect the circuit board to the transistors, and the transistors to the transformer.
Power inverters generally convert a 12-volt input current into a 120-volt output, making them suitable for use in homes and cars. The inverter's oscillator converts the direct current from the battery to an oscillating current, which then enters the transformer. The transformer steps up the current's voltage, resulting in a much higher alternating current leaving the transformer.
Alternatively, build a simple inverter at home using transistors, resistors, a capacitor and a 24-volt transformer. The inverter is powerful enough to power lamps and other small appliances, such as electric shavers, and it shuts down if a device attempts to draw too much power from it. Diagrams for the circuit are available at the Electronic Circuits Archive website.
Once the inverter is built, add an optional extra power supply and transformer to charge the battery. Test the circuit with a 100-watt light bulb, running the main battery until it is flat. Use a voltage meter to ensure that the battery is charging.