I really enjoyed it when my EE professors would simply erase components of a circuit diagram if they didn't matter and they made things complicated. I think that had an impact on my approach to solving problems.
Another trick of the trade is working back from the desired output by stages. For example, for an amplifier delivering 200 W to loudspeakers (or 1 kW to an antenna, or ...), first design the final stage, then work back from that adding the stages needed until the range is OK for the input signal you have.