how can I insert an arbitrary sha256 hash into the blockchain?
You can encode any arbitrary data using the Bitcoin script's OP_PUSH and OP_DROP commands. For this, however, you would need some custom Bitcoin client, as the standard one does not allow you to send messages like this.

Alternatively, you could just use the hash as a part of the generation of a Bitcoin address and store it in the Block chain by destroying one satoshi on it.

There should be a topic covering encoding of any data into the Blockchain somewhere on this StackExchange, so you can also have a look at that.