Circuit simulation can save you a lot of grief when designing advanced circuits. Instead of building something then wondering why it doesn’t work, a simulator can speed up the debugging process by letting you quickly change component values to see how the circuit responds. LTSpice IV is a freely available circuit simulation package from Linear Technology.
The first video shows you how to build a simple low pass filter and sweep through a wide range of frequencies to create a bode plot. It’s a lot simpler than it sounds! The second video demonstrates how you can change component values and add in extra components in your simulation and see how it affects a band pass filter. The third video is about transient analysis simulation, which is arguably the most important thing to know because it provides you with detailed voltage & current graphs for every single node in your circuit!
Bonus: Circuitlabs allows you to do online circuit simulation. Here is an example with a common emitter amplifier, similar to the one I showed you in the last video.