How out of block chain transactions work, and is there any API for that? i wonder how out of block chain transactions work, because till i know it happens but "is not recommended" (it is what i read on the internet), i want to manage some micro transactions but as it is well known  that the fees of each transaction would eat them up so it would be better out of block chain transactions to deal with them?, is there any API that would help me on this? 

Thanks in advanced for your time.
Off-chain transactions are transactions on any system that's not the blockchain. Micropayment transactions, lightning network transactions and even coinbase-to-coinbase or changetip would count as off-chain transactions.

There are API's to the various services. Lightning network is not live yet and micropayment transactions still need settlement on the blockchain.