Note that the rats nest wires need routing to make it legible.
I assume the ESP8266 has a sleep mode.If so, there is no need to turn off the power.Leo..
High side power switch. (suggestion)
You ignored that didn't you?Can you read that schematic? Let me tell you, you can't.The parts need dragging into a more sensible place. Then the dotted wires which are called rat's nest wires need routing so they are composed of horizontal and vertical sections. Diagonal wires are not acceptable in a schematic.The thing about Fritzing and it is why it is hated on this forum is that to use it you require far more skill than you have when you use it, which happens when you feel you need a physical layout diagram. So you make substitutions and render it all useless. By you I mean one, not you personally.Where is the 5V coming from?The problem with this is the connections to the Arduino. When the output is high you feed 5V into a 3V3 system, this is very bad. When the output is low the Arduino is feeding a negitave voltage into the ESP, due to the voltage drop across the FET.Either of these can be enough to latch up the ESP and stop it working.The use of power switching from the top like in reply #10 will solve the negitave voltage situation. A potential divider of 510R and 1K will cut down the 5V output signal from the Arduino to the ESP to 3V3. Finally you need to make that output signal into an input before removing the power, and make it an output again once the power has been restored.
Regarding these transistors, can they be used to switch on/off the (+) instead of (-) is there any limitation for this ?
If you're considering using the 2N3904 as a high side switch (emitter follower), then there will be a considerable voltage drop from the collector to emitter. It won't work for this application. However, it could be combined with a P-channel MOSFET to create a high side switch as in replies 5 and 8.
Do you know the symbol for a transistor? The connection to R3 is called the base, the one with the arrow is called the emitter and the one with no arrow is called the collector.