If you don't know about Transistors, you can visit my earlier Instructable about Transistor as a touch switch. This is the link - https://www.instructables.com/id/Touch-Switch-Using-Transistor/
Don't mistake this circuit with a Darlington Transistor circuit. A Darlington Transistor circuit is a dual Transistor circuit where one Transistor is connected to another one in such a way that as the first one amplifies signals, the second one amplifies it further. But in this circuit, there are actually two mini circuits, where only one of them can be in stable or powered state. It is also known as a Flip-Flop circuit. It is described below.
In electronics, a flip-flop or latch is a circuit that has two stable states and can be used to store state information. A flip-flop is a bistable multivibrator. The circuit can be made to change state by signals applied to one or more control inputs and will have one or two outputs. It is the basic storage element in sequential logic. Flip-flops and latches are fundamental building blocks of digital electronics systems used in computers, communications, and many other types of systems.
Flip-flops and latches are used as data storage elements. A flip-flop is a device which stores a single bit (binary digit) of data; one of its two states represents a "one" and the other represents a "zero". Such data storage can be used for storage of state, and such a circuit is described as sequential logic in electronics. When used in a finite-state machine, the output and next state depend not only on its current input, but also on its current state (and hence, previous inputs). It can also be used for counting of pulses, and for synchronizing variably-timed input signals to some reference timing signal.
Flip-flops can be either simple (transparent or opaque) or clocked (synchronous or edge-triggered). Although the term flip-flop has historically referred generically to both simple and clocked circuits, in modern usage it is common to reserve the term flip-flop exclusively for discussing clocked circuits; the simple ones are commonly called latches.
Using this terminology, a latch is level-sensitive, whereas a flip-flop is edge-sensitive. That is, when a latch is enabled it becomes transparent, while a flip flop's output only changes on a single type (positive going or negative going) of clock edge.
Step 1: The Components
The components can be bought from Banggood. Links of the components are given as follows:
1. 2N2222A NPN Transistor (2pcs) - https://m.banggood.com/50Pcs-TO-92-30V-0_6A-2N2222A-Triode-Transistor-NPN-2N2222-Switch-Transistors-p-1069780.html?rmmds=search
2. LED (2pcs) - https://m.banggood.com/375pcs-3MM-5MM-LED-Light-emitting-Diode-Beads-Resistance-Lights-Kits-Bulb-Lamp-p-1027601.html?rmmds=search
3. 10K OHM Resistor (4pcs) - https://m.banggood.com/560-Pcs-1-ohm-to-10M-ohm-14W-1-Metal-Film-Resistor-56-Value-Assorted-Kit-p-1072159.html?rmmds=search
4. 9V Battery (1pc) - Non-Rechargeable - https://m.banggood.com/9v-Universal-Eastpower-Battery-for-Multimeter-Thermometer,etc-p-78472.html?rmmds=search
Rechargeable (Direct Plug-in System) - https://m.banggood.com/ZNTER-S19-9V-400mAh-USB-Rechargeable-9V-Lipo-Battery-p-1070703.html?rmmds=search
5. 9V Battery Cap (1pc) - https://m.banggood.com/5Pcs-175mm-9V-T-Type-I-Type-Battery-Buckle-Connector-Snap-Clip-Lead-Cable-p-1313739.html?rmmds=search
6. Push Button/Switch (2pcs) - https://m.banggood.com/100pcs-Mini-Micro-Momentary-Tactile-Tact-Switch-Push-Button-DIP-P4-Normally-Open-p-917570.html?rmmds=search
7. Jumper Wires (4pcs) - https://m.banggood.com/120pcs-20cm-Male-To-Female-Female-To-Female-Male-To-Male-Color-Breadboard-Jumper-Cable-Dupont-Wire-Combination-For-Arduino-p-974006.html?rmmds=search
8. Breadboard (1pc) - https://m.banggood.com/Wholesale-Test-Develop-DIY-830-Point-Solderless-PCB-Bread-Board-For-MB-102-MB102-p-51331.html?rmmds=search
9. 5V Buzzer (If you want instead or with LEDs in the circuit) (2pcs) - https://m.banggood.com/10Pcs-5V-Electromagnetic-Active-Buzzer-Continuous-Beep-Continuously-p-943524.html?rmmds=search
Attention, remember, the amount of components in the brackets are required amount, not amounts to buy. You may have to buy more then required, because some of these components are sold in packs in Banggood. And I think you should buy them as packages so that you do not have to buy them again in the future if needed. And remember, that the colour code of 10K OHM Resistor is Brown, Black, Orange, Gold. Other types of Resistors will have different colour codes.
Step 2: The Connections
This is a dual Transistor circuit, which means that it uses two Transistors. As it is based on Transistors, you'll need to know what they are and how they behave. You'll get to know about them in my earlier Instructable about Transistor as a Touch Switch circuit. Here's the link - https://www.instructables.com/id/Touch-Switch-Using-Transistor/
This Instructable is about Transistor SR Latch circuit, also known as a Flip-Flop circuit. Let's make it.
First, take two 2N2222A NPN Transistor. If the flat side of this Transistor faces you, the leftmost of the 3 pins would be Emitter, middle one the Base, and the rightmost pin would be the Collector. Remember this. Insert the two of them to the breadboard keeping short distance between them, so that the pins of the resistors can be connected to the Transistor. Before starting, make sure to watch breadboard tutorials if you don't know how to use them. As you insert the Transistors to the breadboard, remember to keep their Emitter at the left side, so that the flat side of the Transistors face you. Gather 4 10K/1000 OHMs resistors. Connect one of them to the Base of the first Transistor and to the Collector of the second Transistor. Then connect another resistor to the Base of the second Transistor and to the Collector of the first Transistor. Remember, VCC means positive power supply and GND (Ground) is the negative point which ends/completes a circuit. Take the third resistor and connect it to the first Transistor and to the breadboard VCC rail/bus. Do the same with the fourth resistor and the second Transistor. Then take two LEDs. Now there's a little problem. Taking two different coloured Transistors might sometimes create problems in switching from one stable state LED to the other because different coloured LEDs have different voltages. Connect same coloured LEDs to avoid problems, and after the circuit is successfully working, you might change the colours. Take the first LED and connect it's Anode (+) to the Collector of the first Transistor and Cathode (-) to the Emitter of the first Transistor. Do the same with the second LED. Then take a jumper wire and connect it with the Emitter of the first Transistor and to the negative rail/bus of your breadboard. Do he same with the second Transistor. Then take two push buttons/switches. Take one of them and connect one of it's pins to the breadboard's negative rail/bus, and the other pin should be connected to a disconnected place of the breadboard. Do this with the other one too. Then take two more jumper wires. Connect the first one to the first Transistor's Collector and to the disconnected pin of one of the switches. Then do the same with the second jumper, second Transistor and the other switch. And, you're done.
Step 3: Finished - Let's Test the Circuit
You've finished making your circuit. Now connect the 9V Battery Cap's VCC (Red wire) to the positive breadboard bus and GND (Black wire) to the negative breadboard rail. Then connect the 9V Battery with the Battery Cap. You're done. You'll see that one LED will be on, and as you press the switch of the other LED, the former LED would turn off, turning the other LED on. You've completed making and testing your Flip-Flop Circuit. Good luck for your experiment.