How to transfer a NFT from one account to another using ERC721?

You can use just the _transfer() function, see my buy() function for an example of implementation.

The approvals for sale can be done using a custom mapping - in my example tokenIdToPrice. If the value is non-zero, the token ID (mapping key) is for sale.

This is a basic code that allows selling an NTF. Feel free to expand on my code to allow "give away for free", "whitelist buyers" or any other feature.

pragma solidity ^0.8.4;

import 'https://github.com/OpenZeppelin/openzeppelin-contracts/blob/master/contracts/token/ERC721/ERC721.sol';

contract MyToken is ERC721 {
    event NftBought(address _seller, address _buyer, uint256 _price);

    mapping (uint256 => uint256) public tokenIdToPrice;

    constructor() ERC721('MyToken', 'MyT') {
        _mint(msg.sender, 1);
    }

    function allowBuy(uint256 _tokenId, uint256 _price) external {
        require(msg.sender == ownerOf(_tokenId), 'Not owner of this token');
        require(_price > 0, 'Price zero');
        tokenIdToPrice[_tokenId] = _price;
    }

    function disallowBuy(uint256 _tokenId) external {
        require(msg.sender == ownerOf(_tokenId), 'Not owner of this token');
        tokenIdToPrice[_tokenId] = 0;
    }
    
    function buy(uint256 _tokenId) external payable {
        uint256 price = tokenIdToPrice[_tokenId];
        require(price > 0, 'This token is not for sale');
        require(msg.value == price, 'Incorrect value');
        
        address seller = ownerOf(_tokenId);
        _transfer(seller, msg.sender, _tokenId);
        tokenIdToPrice[_tokenId] = 0; // not for sale anymore
        payable(seller).transfer(msg.value); // send the ETH to the seller

        emit NftBought(seller, msg.sender, msg.value);
    }
}

How to simulate the sale:

1. The contract deployer (msg.sender) gets token ID 1.
2. Execute allowBuy(1, 2) that will allow anyone to buy token ID 1 for 2 wei.
3. From a second address, execute buy(1) sending along 2 wei, to buy the token ID 1.
4. Call (the parent ERC721) function ownerOf(1) to validate that the owner is now the second address.

If you let anyone call the approve function, it would allow anyone to approve themselves to take NFTs! The purpose of approve is to give the owner of an asset the ability to give someone else permission to transfer that asset as if it was theirs.

The basic premise of any sale is that you want to make sure that you get paid, and that the buyer receives the goods in return for the sale. Petr Hedja's solution takes care of this by having the buy function not only transfer the NFT, but also include the logic for sending the price of the token. I'd like to recommend a similar structure with a few changes. One is so that the function will also work with ERC20 tokens, the other is to prevent an edge case where if gas runs out during execution, the buyer could end up with their NFT for free. This is building on his answer, though, and freely uses some of the code in that answer for architecture.

Ether can still be set as the accepted currency by inputting the zero address (address(0)) as the contract address of the token.

If the sale is in an ERC20 token, the buyer will need to approve the NFT contract to spend the amount of the sale since the contract will be pulling the funds from the buyer's account directly.

pragma solidity ^0.8.4;

import 'https://github.com/OpenZeppelin/openzeppelin-contracts/blob/master/contracts/token/ERC721/ERC721.sol';
import 'https://github.com/OpenZeppelin/openzeppelin-contracts/blob/master/contracts/token/ERC20/IERC20.sol';

contract MyToken is ERC721 {
    event NftBought(address _seller, address _buyer, uint256 _price);

    mapping (uint256 => uint256) public tokenIdToPrice;
    mapping (uint256 => address) public tokenIdToTokenAddress;

    constructor() ERC721('MyToken', 'MyT') {
        _mint(msg.sender, 1);
    }

    function setPrice(uint256 _tokenId, uint256 _price, address _tokenAddress) external {
        require(msg.sender == ownerOf(_tokenId), 'Not owner of this token');
        tokenIdToPrice[_tokenId] = _price;
        tokenIdToTokenAddress[_tokenId] = _tokenAddress;
    }

    function allowBuy(uint256 _tokenId, uint256 _price) external {
        require(msg.sender == ownerOf(_tokenId), 'Not owner of this token');
        require(_price > 0, 'Price zero');
        tokenIdToPrice[_tokenId] = _price;
    }

    function disallowBuy(uint256 _tokenId) external {
        require(msg.sender == ownerOf(_tokenId), 'Not owner of this token');
        tokenIdToPrice[_tokenId] = 0;
    }
    
    function buy(uint256 _tokenId) external payable {
        uint256 price = tokenIdToPrice[_tokenId];
        require(price > 0, 'This token is not for sale');
        require(msg.value == price, 'Incorrect value');
        address seller = ownerOf(_tokenId);
        address tokenAddress = tokenIdToTokenAddress[_tokenId];
        if(address != address(0){
            IERC20 tokenContract = IERC20(tokenAddress);
            require(tokenContract.transferFrom(msg.sender, address(this), price),
                "buy: payment failed");
        } else {
            payable(seller).transfer(msg.value);
        }
        _transfer(seller, msg.sender, _tokenId);
        tokenIdToPrice[_tokenId] = 0;
        

        emit NftBought(seller, msg.sender, msg.value);
    }
}

// mapping is for fast lookup. the longer operation, the more gas
mapping(uint => NftItem) private _idToNftItem;

function buyNft(uint tokenId) public payable{
    uint price=_idToNftItem[tokenId].price;
    // this is set in erc721 contract
    // Since contracts are inheriting, I want to make sure I use this method in ERC721
    address owner=ERC721.ownerOf(tokenId);
    require(msg.sender!=owner,"You already own this nft");
    require(msg.value==price,"Please submit the asking price");
    // since this is purchased, it is not for sale anymore 
    _idToNftItem[tokenId].isListed=false;
    _listedItems.decrement();
    // this is defined in ERC721
    // this already sets owner _owners[tokenId] = msg.sender;
    _transfer(owner,msg.sender,tokenId);
    payable(owner).transfer(msg.value);
  }

this is Nft struct

struct NftItem{
    uint tokenId;
    uint price;
    // creator and owner are not same. creator someone who minted. creator does not change
    address creator;
    bool isListed;
  }