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Advice on getting Started: Go through this Workbook.
QUCS can be used to simulate analog circuits, digital circuits, and can even import well known types of circuit descriptions (e.g. VHDL, Verilog, SPICE, etc).
The software takes some getting used to, and it has some quirks about dealing with singularities (e.g. divide by zero) that occur during simulations. If a simulation hangs for a very long time, it has likely encountered an unsolvable singularity. Press cancel, and re-work your circuit. Often times, inter-changing Voltage or Current sources can cause/fix the singularity. Using square wave sources can also lead to singularities. Diodes also open up possibilities for singularities.
You can download an example of a Bandpass Filter that Matt made for the NYUAD workshop 2011.