Dead bug soldering is a style of soldering circuits without using a Printed Circuit Board (PCB).
Typically, the goal is to just wire up the circuit so it works, but what if we arrange the components in such a way so it looks like something... say a dog?!

Step 1: Tools and Parts List

Of course you will need a soldering iron, solder, wire stripper, flush cutters, and optionally a helping hand (third hand) to hold pieces while you solder them.

Parts:

1 x 555 Timer Chip
1 x LED
1 x 470 ohm Resistor
1 x 4.7uF (16V or higher) Electrolytic Capacitor
1 x 10K Resistor
1 x 100K Resistor
1 x 9V battery
Some connecting wire

Step 2: Tinning the Chip

The 555 Timer chip is the center piece of our sculpture. It is easier to solder leads if they already have some solder on them. So let's put some solder on the chip legs. This is called tinning. Heat up the chip leg with the iron, then melt a little bit of solder onto them. The solder should look shiny.

Step 3: Schematic

You can use your creativity and arrange the parts any way you wish in whatever order, but let me share how I did mine.

Step 4: Dog's Right Rear Leg

I chose to solder the capacitor first because it is bulkier than the resistors. I figure it would be easier to match the other dog legs to this bulky component rather than the other way round.

Negative leg of the capacitor should be soldered to pin 1 and the positive leg onto pin 2.

Step 5: Dog's Head

Cathode (shorter leg) of the LED becomes the dog's tail and should be connected to the negative side of the capacitor and pin 1 of the chip. We will solder the Anode (longer leg) of the LED in the next step.

Step 6: Dog's Right Front Leg

The dog's front right leg is the 470 Ohm Resistor. There is no polarity to worry about on resistors, but cosmetically, I thought it looks better if the bulk of the resistor is in front rather than the other way round.

One resistor leg goes to the Anode of the LED, and the other resistor leg goes to pin 3 of the chip.

Step 7: Dog's Front Left Leg

Dog's front left leg is a 100K Ohm resistor between pin 6 and 7 of the chip. Note that using the extra lead of the resistor, we also connect pins 2 and 6. Make sure that the crossed wires do not touch each other.