Counter with line decoder
Here's a more refined counter circuit that counts up to three and uses three LEDs to indicate the count. It's a bit more difficult to count to three using three LEDs instead of two, so we have to acid another circuit known as line decoder to the counter circuit.
You can locate the line decoder in the schematic, it's the group of NAND gates connected to the three LEDs, You probably recognized the multivibrator circuit in the schematic.
When you put the power ON, you'll see LEDs 1, 2 and 3 light on and off in order.
The counter circuit is ... (canyon guess? Don't peek.)
Here's a brain exercise that'll really keep you going for a while ... canyon trace the 0 and 1 inputs from the multivibrator and follow them through the counter to the LEDs?
It's not that difficult to trace and it will give you a good idea how a counter circuit like this works. Try it and see.