1. Extend the ERC20 contract to create a new burnable token contract:

pragma solidity ^0.4.23;

import "./ERC20.sol";

contract Burnable is ERC20 {
    ...
}

2. Create a function that can be called by the user to burn some tokens:

function burn(uint256 _value) public { }

3. Verify whether the sender has enough balance to burn:

require(_value <= balances[msg.sender]);

4. While burning tokens, subtract the number of tokens burnt from the balance of the current holder and from total supply:

balances[_who] = balances[_who].sub(_value); 
totalSupply_ = totalSupply_.sub(_value);

5. Emit an event for every token burning transaction. Create a burn event with the sender address and value as parameters:

// Event declaration
event Burn(address indexed burner, uint256 value);

// Emit the event during burning process
emit Burn(msg.sender, _value);

6. It is also recommended to emit the transfer function that marks a transfer to the null address. Transferring a token to the null address makes it unusable:

emit Transfer(msg.sender, address(0), _value);

7. Modify the contract further by creating an internal function that allows other contracts to burn tokens for users. This can improve the reusability of the function:

pragma solidity ^0.4.23;

import "./ERC20.sol";

contract BurnableToken is BasicToken {

    event Burn(address indexed burner, uint256 value);

    /**
     * @dev Burns a specific amount of tokens.
     * @param _value The amount of token to be burned.
     */
    function burn(uint256 _value) public {
        _burn(msg.sender, _value);
    }

    /**
     * @dev Internal function for burning tokens.
     * @param _user Address to burn the tokens from.
     * @param _value Amount of token to be burned.
     */
    function _burn(address _user, uint256 _value) internal {     
        require(_value <= balances[_user]);

        balances[_user] = balances[_user].sub(_value);
        totalSupply_ = totalSupply_.sub(_value);
 
        emit Burn(_user, _value);
        emit Transfer(_user, address(0), _value);
    } 
}