A pit gain, flow with the pumps off, or a drop in pump pressure can be the sign. Gas, oil, or formation water are all kicks. The response is to shut the well in and circulate the influx out under control, holding enough pressure that the bottom of the hole stays at or just above pore pressure.
If the influx is not stopped, it can unload the mud and become a blowout. Swabbing while pulling pipe, drilling into an unexpected pressure, and losing the fluid level during total losses are the common ways a kick starts. A kick is the event. Well control is the response.