You can easily blink the LED with arduino or 555 timer. But You can make a blinking circuit without such ICs. This is an simple blinking figure made from discrete parts.

Supplies

NPN transistor

2sc1815 x 2 or any little NPN transistor

Capasitor

47μF x 2

Resistor

4.7KΩ x 2 , 1KΩ x 1 , 100 Ω x 1 , 0 Ω x 1

Battery

CR2032 x 1

Red , Green or Yellow x 1

Copper plate
Solder wire

Step 1:

This is a circuit diagram. It is called "astable multivibrator". If you are interested, google it with this word.

Step 2:

Putting the parts on paper will reduce mistakes.

Step 3:

Transistors, LED, and capacitors have a fixed direction. Especially for transistors, the pin arrangement differs depending on the type, so it is recommended to check the datasheet.

Step 4:

Refer to the figure for how to arrange the parts. I recommend to use breadboard as a jig.
Insert the E pin of the transistor into a breadboard, and solder the B pin to the negative side of the capacitor, the C pin to the positive side, the LED, and the resistor in this order. The 0Ω resistor is used as a stick that the figure holds in his hand. It may be just a copper wire.

Step 5:

Make sure you haven't forgotten the solder and that it hasn't shorted.
Let's turn on the power. Put CR2032 negative side to Copper plate , stand figure on the Copper plate and stick that the figure holds to top of the battery .

Step 6:

Figure that I made was blinked about 4Hz speed. If you want to change speed. Try change type of part.
For example

4.7KΩ Resistor to 10kΩ or 47kΩ , blink speed will slow
47μF Capasitor to 100μF, blink speed will slow

Introduction: Tiny LED Blinking Figure