Implementing a Blockchain at the very basic level?
Bitcoin Core is a software which maintains the blockchain ledger, You can obviously fork it and go through the entire code and make some changes to the source code to make your own blockchain (This is what every blockchain company is doing nowadays under the pretext of creating blockchain technologies.) 

However, the above mentioned task is really time consuming. What you can do is study the workings of the bitcoin blockchain, and simulate them using a more popular database. There have been cases where people have sold their 'blockchain' technology with SQL running at the back. Blockchain is basically a database(highly replicated) and you shouldnt confuse it with anything else.  

So trying to make a blockchain from scratch will obviously take a lot of time in learning and then coding. If you are going with the "hidden SQL" blockchain , or for that matter any other db, you would need to make APIs to access the blockchain(just like bitcoin core). You dont need to have all the API's obviously, but the ones which are crucial for the blockchain you'll have to emulate.