Q:

How would I use Arduino microcontroller separately?

I'm learning Arduino. I use Arduino Uno board with ATMEGA328-PU. I tried basic codes like LED blink, control of DC motor etc. Arduino board is used only when we program microcontroller, right? I mean, when we finish programming it, we can use microcontroller separately? If it can be used separately, we must have some "external" circuit as replacement for Arduino board, which allow us to use microcontroller in specific application. What type of circuit is used? I'm new in this field so don't blame me because of amateur questions.

A:

Assuming you are going to upload the program into the ATmega328 on the Arduino, then take the ATmega328 out of the socket, and use it in your circuit, then a simple answer is to search for "minimal Arduino circuit"
An example returned by that search is "From Arduino to a Microcontroller on a Breadboard".
It lists:

a 16 MHz crystal,
a 10k resistor, and
two 18 to 22 picofarad (ceramic) capacitors

That is enough to run the chip at the same speed as the Arduino, and the code used on the Arduino to initialise its clock will work unchanged.
This should run okay directly from a battery supply of about 4.5V or 4.8V, or a good 5V power supply.
A better circuit, which runs at the same 16MHz speed as the Arduino is 'Shrimp It'. That shows a similar minimal circuit and a better 'protected' circuit which has a more reliable approach for its power supply. This is all you need to run off a 4.5V (e.g. 3 1.5V) battery power supply.
However, if you don't care about running at 16MHz, you could ditch the crystal and capacitors, and use the internal 8MHz oscillator, that will need the code to be slightly different. For example, the 8MHz clock is 1/2 the speed of the Arduino's standard 16MHz, so code like delay() will take 2ms instead of 1ms.
Further, the RESET button can be set up so it doesn't need the 10k pullup.
So, with some software changes (search the web for details), an ATmega328 could be used with no external components. 
Alternatively, you might want to use a better power supply, for example a voltage regulator with the circuit of the protected 'Shrimp It', and be able to load the program onto the ATmega while on its board. 
There are products which bundle that 'standard' set of parts (voltage regulator, plugs and sockets and protected 'Shrimp It' running exactly like an Arduino at 16MHz) with a very compact PCB. They are able to plug directly into a breadboard, and so can be used with veroboard/stripboard (or a PCB) to make the rest of the circuit.
One is a kit called 'Boarduino'from adafruit. That web site gives some details to sow how to do this yourself. It is a convenient-to-use version of the 'Shrimp It', on a compact PCB. 
An alternative kit is the "Really Bare Bones Board (RBBB) kit". However it is available as the PCB only, which is the "Really Bare Bones board (RBBB)", though the same supplier as the RRRB kit.
Neither Boarduino nor RRRB has on-board USB upload circuit. However, you can use your Arduino to do that, for example "Using an Arduino as an AVR ISP (In-System Programmer)". Or you could buy a USB to UART cable.

