First thing you have to do before you remove your engine and drive line is to make sure you have plenty of hand cleaner and somewhere to wash up where you won't get killed for making a mess, because you are about to get seriously dirty. Most old engines are balls of old grease, oil and dried fluids mixed with serious amounts of road dirt, under which lies every nut and bolt that you are going to have to remove.
Washing the engine down with degreaser before you start removal may work with those engines which are more lightly encrusted, but if you have a seriously dirty motor, degreaser will only slime up the outer surface.
Different engines and layouts will require a different order in the following steps but in any car there is a logical progression.
First you will have to remove the engine's peripherals. Off come the carburetor, generator/alternator, starter, the fan etc., and it is either a good idea or absolutely required that you remove the radiator. Clean away wiring harness and anything which could possibly get in the way when you eventually try to lift the engine. Don't get lazy. If anything can snag your motor during the lift it will, so the more you take off or secure out of harm's way, the less aggravation and pinched fingers you are going to have.
You will need to make the decision early on whether you are going to lift the engine out with the transmission on or off. With a lot of cars it is more aggravation to get under and separate the engine and transmission than it is to remove them as a complete unit. With pre war cars with large motors like Packard's make sure that you have an engine hoist capable of lifting the combined weight. If you have a small lift that you aren't sure of, put up with the added work and pull the transmission before you pull the engine out. A popped seal in a hydraulic lift will result in a very heavy engine crashing to earth and crushing anything under it with no consideration to it being made of metal or flesh.
Of course the exhaust pipe has to be removed along with the exhaust manifold. It is dumb to remove the engine with the manifold on unless you intend to replace it and know replacements are easy to get. The cast manifolds are fairly delicate and easily cracked during engine removal so get them off. You'll probably find this removal of the exhaust the most incredibly annoying part of the whole job. I know that I have become quite cranky a number of times during this stage and I can think of one car I walked away from for a number of weeks so that I wouldn't beat it to a pulp. The constant heating and cooling of the exhaust plays havoc on nuts and bolts. They flake until they are no longer the original size or shape. Forcing a smaller socket over a nut can sometimes get it to turn, but in most cases it just removes more rust and the socket spins on the eroded nut. Of course getting vice grips on may work but I'll bet you that if you can get grips on most of the nuts, the worst one will be inaccessible to any kind of clamping pliers invented by man. Hammer and chisel is a last resort and usually just an exercise in frustration. If you cannot make any headway the only solution is a cutting torch wielded by someone who knows what they are doing. If you are good with a torch and reading this then you already know the drill. If you aren't then this is not the time to learn. An inexperienced torch can do too much damage. Time to call for help. There will likely be local mechanics quite capable and perhaps willing to make a trip out if you get stuck. If not then you will likely have to call in a welding service to do the cuts for you. Just make sure they don't cut any thing that you need to keep. It is best that just the bolts and nuts are cut but if that proves impossible use your best judgment to cut the system off where it will do the least damage and be easiest to remedy later. Damage as little as possible.
In most cases the engine will have one central or two side engine mounts on the engine itself, with an additional pairing of mounts or a single central mount on the transmission. If you are removing the transmission then you will have to support the back of the engine until you are ready to remove it.
Most mounts have rubber pads insulating the engine from the chassis. These will usually have to be replaced before you reinstall the engine, as they are rarely reusable. Once you have liberated the bolts from the engine mounts you are ready to lift the engine.
Attaching the engine hoist to the engine can be a bit perplexing. Now here are some important warnings. On most V 8 engines you will have numerous bolt holes on the front and back of the head castings. These, although convenient, make really bad attachment points, as what often happens is that as the engine lifts the cast snaps and the bolt flies from the hole with the result that you drop the engine, usually on the car or worse, on some part of you or a helper.
Any attachment points you use have to be straight to the direction of pull, meaning that you should lift the engine using holes found on the top. If you don't have many then remove an already existing bolt from its hole. Head bolt holes are good as long as you put your lifting bolt a long way into the tread. Don't use a bolt, which only catches a few threads even if you don't have anything else. Properly secured you won't do any damage. Improperly secured you can end up with all kinds of messes from having the engine fall back in the hole and jam to a quick trip to the hospital.
Also secure your lifting bolts so that the engine is going to balance fairly well. Front left to right rear sort of idea. Attach your chain to the hoist on the link that will best balance the whole affair level, then you can manipulate it side to side and up and down as you need to remove it while having the engine want to swing back to level.
It is possible to pull an engine out by yourself but it is so much easier done as a team sport. A helper or two can watch for snagging and help you push and pull the engine just where it needs to be as it comes up. At a certain point it will finally swing free and be completely liberated from the car. At this point you will need to lift the engine high enough to clear the front of the car. Plan this carefully. You can get into trouble trying to manhandle an engine over an obstruction that the hoist can't clear. You will also need to pull the hoist back and away from the car. This is very hard to do on a dirt driveway or on soft asphalt into which the small steel wheels of the hoist will sink. Making a track way from heavy plywood or doing the lift on a concrete garage floor is the best way to go.
Now some of you will want to use a chain fall, and where available these are a great way to pull an engine but don't just assume the two by fours in the garage are capable of holding the weight of an engine, transmission and the chain fall itself. Just remember with a chain fall you will have to move the car away from the engine. Seems like a dumb warning? I know a guy who lifted his motor out with the front of the car in the garage door so that he had lots of light. Unfortunately the rest of the car was in the garage. The result. The engine wouldn't lift high enough to roll the car under so it had to go back in and the car had to be turned around. More work and of course far worse, the continued voicing of admiration from others who were in attendance.
Once you have the motor out you can separate the transmission, and then mount the engine on an appropriate engine stand if you are going to do more work yourself, or send it off to be rebuilt if not.
Now you have a great big cavernous hole in the front of your car and it is much easier to push around.
Next step. Get the paint off.