Blockchain handles Double spending by confirmation mechanism. Once the transaction is initiated, it is kept in the pool of transactions. Only the first transaction gets confirmations and will be verified by miners. Miners will discard other similar transactions.
But what if both transactions are made simultaneously, the transaction which gets the maximum number of confirmations from miners is included in blockchain while others will get discarded. Receiving parties are advised to wait for at least six confirmations. Once a transaction is made, miner creates a block, add the transaction (along with few others) to the block and then append the block to the blockchain after mining. So, once a minimum of six blocks are added to the blockchain, the receiver is assured that transaction is not double spent as Blocks are mathematically associated with previous blocks.
For making changes to the previous block, one has to reverse the transaction in the last six blocks, which are computationally impossible.
Ref.: Satoshi Nakamoto whitepaper
In Blockchain architecture, an electronic coin is a chain of digital signatures. In the diagram, owner 1 is transferring coin to Owner 2. It happens by digitally signing a hash of the previous transaction and public key of the owner 2 and adding this to the end of the coin. A payee can verify the signature to verify the chain of ownership.
Study Material