NFT minting has a network transaction fee associated with it called ‘Gas’ this is a fee charged by the blockchain to process the minting of the NFT.
As to how much it costs, well it varies from one blockchain to another. So you have the major blockchains that are used to today's minting of NFTs the biggest being ethereum ERC-721 or ERC-7211 here the fees are the highest it could cost $40 during peak times to mint an NFT the lowest I have ever seen is $9 just to mint. That does not include the price of the NFT itself.
Then you have Polygon/Matic and Solana. Now these two blockchains are very efficient and have been designed with low almost zero transaction fees. That does not mean there is no fee it's just so small in comparison to ethereum most investors refer to its no gas mints for Polygon NFT the gas fees will be about $2 at peak and half that during quieter periods. On Solana it is less than a dollar most of the time.
There have been advances on the Ethereum blockchain Azuki, a NFT collection that dropped in early 2022 created their own smart contract code that allowed investors to do multimint at reduced prices.
It's called the ERC-721a (azuki smart contract) this contract has advantages when you minting in batches say you mint two NFTs in one go you will pay the full gas for one and only about 10% of the gas for the second one and it goes on in that same way if your minting 3 you pay the full gas for one and again about 10% for the next two.
This multi minting gas saving contract is now used in drops as it encourages investors to mint multiple NFTs at a time and take advantage of the reduce gas fee.