I pull engines fairly often and I don't like a big mess. The first thing I do is go to the local appliance store and get a large box from a refridgerator to cut up and lay under the car. If one piece gets all soaked with a fluid I've still got 3 more to make another mess! Siphoning certain fluids is another thing I do to keep things clean and neat. Most (but not all) radiator petcocks are not in a place that's both easy to reach and they don't usually pour the fluid in an open enough area to easily collect the fluid without it running all over suspension/steering components or the frame or core support creating multiple waterfalls under the car. So I siphon the radiator. Then I remove one end of the lower hose to drain the rest of the fluid into a bucket without the geyser that happens if the system is full. Then there's usually only a small amount of fluid that spills out when I pull the engine from whats left in the block. On this car I did this before removing the sheetmetal knowing I'd need the fluid out eventually.
Next is the Automatic transmission. Lots of stock trannys require dropping the pan to drain the fluid and it can make a big mess real fast if things go wrong. So I siphon the trans fluid out of the dipstick filler tube opening after removing the filler tube. Then the trans can be removed without dropping the pan and just refilled after reinstalling if there's no need to get into the trans.
With the fluids taken care of (no need to drain oil in this case) I support the trans with a jack and hook up the engine hoist with the chains just snug so the engine and trans can't fall and then remove the bolts holding the engine and trans together, the bolts holding the flexplate to the torque convertor, and the trans crossmember bolts. A slight tweak with a prybar between engine and trans housing slides the trans back far enough to remove the engine. Then remove the engine mount bolts and out she comes!
