Any sudden change in circuit conditions like a step change in input voltage/current, switch closing/opening, parameter variations can induce transients.

An ideal series RL or RC circuit with no resistive losses has no transient behavior and instantly reaches the steady state.

Component values, types and the overall network configuration including presence of feedback decide a circuit's time domain settling behavior.

Laplace transform provides the most direct approach. Other techniques include differential equations, Bode plots, Nyquist criterion etc based on specific circuit configurations.

Underdamped, critically damped and overdamped based on the damping ratio value which determines oscillatory versus monotone settling characteristics.