Downloaded bitcoin core and it says synchronising with network, how do I get it to download the blockchain?
You have not lost the money, "synchronizing with the network" means that your Bitcoin Core is downloading the blockchain! 

This may take a few hours or days depending on the computational power of your computer. If you don't need them immediately, you can just wait until the synchronization is finished which is what I would suggest that you should do. 

If you are anxious to check whether the bitcoins were transferred, you can look up your address (that it was sent to) on one of the block explorers.