There are two drain plugs in the block; one on each side. You might have to pull the starter to access the one on the passenger's side.
Take a look
here for a couple of pictures of the drain plug locations. I would recommend installing petcocks in place of the plugs, to make this easier the next time you do it.
Beyond that, putting a T-fitting in the heater hose going into the cylinder head would help with flushing the system out. I've never tried dishwasher soap, but I used the Prestone Cooling System cleaner with good results. Certainly, you can't flush too much water through the system...when you think you're done, go at it again
And, as the last poster pointed out, a coolant filter's a really good idea. It's inexpensive, and it'll really help with long-term maintenance. Take a look
here for one suggested way to install it, and there are a few other ways also that you can find through a search.
Hope that helps...good luck!
(No, I"m not trying to self-promote; I don't know what you're talking about
)