There are a lot manufactures for the DHT11 this one is made my AOSONG. It can run between between 3 and 5 volts and uses a simple one wire protocol to communicate with other devices. For more details on the sensor itself check out the datasheet.
The casing is in two parts so to get inside it is just a matter of getting a sharp knife and splitting the case apart.
Inside the case is a small PCB with a SOIC 14 packaged IC unfortunately the part number has been removed so there is really no way to tell if this is a custom part or a specially programmed MCU. along the edge of the IC are couple of ceramic capacitors for decoupling and noise suppression, and some other misc passive components. The green resistor I can assume is a precision resistor for the humility sensor (explained in more detail later).
On the other side the sensor hardware itself. This consists of a PCB with interlaced traces that creates capacitance this with change based on the amount of moisture present in the air around it.
HOW DOES IT WORK
The interlaced +ive and -ive traces allow a small amount of charge to be stored in each of the traces allowing the circuit to charge up a little, this is called capacitance and this is effected by the material separating the +ive and -ive which is mostly air and its airs permittivity one of the factors for calculating capacitance is affected by temperature and humidity.
So the chip uses the precision resistor I mentioned earlier and measures the discharge time through that resistor to calculate the capacitance, and then uses that figure used with the internal temperature sensor inside the main IC to calculate the relative humidity.