Safely dispose of dead iPhone
If it appears at all when you connect it to a computer you may be able to restore it to factory settings and wipe all the data using iTunes.

If it was on a recent version of iOS once the phone is powered off if you have had a passcode set and it was a reasonably long alphanumeric one it would be unlikely that any one would have the time and resources to crack the passcode and recover any of the data unless you have drawn the attention of a nation state?  This tweet from respected cryptographer Matthew Green gives an idea of the time taken to crack a passcode depending on it's length.

I have heard stories of people putting iPhones in the microwave to render them unusable but can't recommend this from a safety perspective.

If it is still signed into your iCloud account and you have Find My iPhone enabled you could it to erase the phone on the off chance someone finds it and is able to get it working again.

Once you are happy it is wiped or data is unrecoverable take it to an Apple store and they will recycle it for you or even offer you a rebate on a new phone if you are buying one.  See here for more details.

If you are not at all concerned with it being recycled, which would be a shame, or there was anything on that sensitive you cannot risk the slightest chance of anyone finding the phone, take a drill/ hammer to it.