The 555 Timer can be used in several different modes.
Here we are going to use it in a Monostable (generates an output pulse) configuration.
Here are a useful link of some great resources for understanding the 555 Timer.
Step 1: Time Calculation
For my project I wanted a delay of approximately 3 Seconds.
The calculation for the time is t = 1.1 * R (Resistance in ohms) * C (Capacitance in Farads)
In my circuit I have a 3M ohm resistor and a 1 micro Farad capacitor.
That's 3000000 Ohms and 0.000001 Farads
so time(t) = 1.1 * 3000000 * 0.000001
t = 3.3 Seconds
Here is a handy calculator
Step 2: Full Circuit
Here is the full circuit schematic.
In this circuit there are two relays, one is driven by an external input which then drives the trigger signal the other is driven by the output of the 555 timer. When the input goes high the relay turns on when the input signal turns off there is a 3.3 Second delay before the relay turns off.
Step 3: PCB Layout
Here is the PCB layout this can be uploaded to a PCB fab service such as www.OSHPark.com