In the following pictures, the Esp8266's Rx is connected to the Uno's Rx.

In the following pictures, the Esp8266’s Rx is connected to the Uno’s Rx. Is this a mistake?
Secondly , the esp8266 uses 80mA, however, the uno only provide 20mA! Should I add a transistor in the 3.3v pin of the uno?

the rxd and txd lines need to be crossed. txd is the sender (Talker) and needs to be connected to the Receiver at rxd

@Marvin_Sielenkemper so the above picture is wrong?

yes

and a transistor wouldn’t really help there, I’m afraid. what would you connect it to? It can not produce power which is not there.

I thought a transistor can amplify the current

hm. but the current has to come from somewhere. the current a transistor draws on the emmiter depends on the current supplied on the basis. that is where the amplification happens. there is no magical multiplication of current…

So I should use a battery that can supply 80mA and add some resistor so it becomes 3.3v ?

just a resistor would not work. the esp does not constantly draw 80mA. and if it uses less, the resistor would not lower the voltage enough which might damage the esp. you need a voltage regulator.

how do you power the arduino?

With 4 AA batteries

And then I connect them to the jack on the Arduino

so about 6v which is a bit on the low side…

Yea, I do realize that, but I haven’t found a battery box that holds more battery, so I will use 4 AA batteries for now.

You could try something like that (emitter follower):

So yes, just add a transistor: NPN, 500mW, 20V, beta of about 100 or more.

Ok, thank you

The Arduino’s GPIO pins can only supply 20mA of current. The esp8266 is connected to the Arduino’s 3.3V pin which can supply much more current. You’ll have to check the datasheet of the 3.3V regulator, but I think it’s somewhere around 200mA. You’re totally safe powering the esp8266 from the Arduino’s 3.3V pin.

As far as the UART goes, (Tx/Rx lines) if you’re trying to have the two devices talk to one another you need to have tx from one go to rx of other and vice versa. Hope this helps.

I have done the connection right , and realize I it’s port is appearing in my mac , after some research, I know it’s because there isn’t enough current to power it. So is there any method of connecting the esp8266 with out a transistor?
Secondly, I couldn’t find the flasher for esp8266 for Mac, anyone found it?

I use esptool.py on the Mac. https://github.com/espressif/esptool