Teardown & Cleaning
First confirm the year and model engine you are rebuilding. Do not order any parts for this engine before you tear it down. The reason is, you may not be able to rebuild it. I have found that as many as one out of every ten engines I have torn down were not worth rebuilding. Also, there is no way to know what size pistons/ rings or bearings to order.
Before you start to remove the engine, clean it as best you can. Ask around if you don't have a pressure washer. Sometimes you can find a shop who has a steam cleaner or even a friend with a plain pressure washer.
Before you remove anything, confirm that your manual has a good layout of all the vacuum hoses or the sticker under the hood is still readable. Even so it is a good idea to put masking tape on each hose end and on each wire end as to it's location. Also note on a pad where each goes before you remove anything. Read the manual as to what has to come off and what don't. If it has AC, look closely at the compressor and hoses to see if it is possible to leave the hoses connected and just pull the compressor aside and tie it out of the way. The same with the condenser and dryer if they need to be removed. Many times the manual says to evacuate the AC system and remove the compressor but I found many can be just unbolted from the engine and tied over out of the way. If the AC system needs to be opened you MUST take the car to a shop that has the retrieval system to remove the gas (134 or R-12) which ever it has. When you finish you can go back to that shop and get the AC system evacuated and recharged. Keep in mind that 134 is poisonous.
Remove the battery if it is close to what needs to be removed to get the engine out. If it is mounted out of the way, you can just remove the cables. If the radio is a programmable radio or any other computer needs to stay connected you should get an accessory battery from most auto parts stores. If the large wire on the alternator is a bolt-on, be sure to tape it up or slip a piece of rubber hose over it so as not to short out the small battery. You may want to reconnect the battery after you get the engine out as the small accessory battery may not be good for the time you will have the engine out. You may even want to charge the battery if the engine job turns into a long project.
Drain the coolant into a container with a lid and clean up any spills right away. Antifreeze is very appealing to pets and is very poisonous.
If the car is automatic be sure to unbolt the torque converter from the flex plate (flywheel) and be careful to keep pushing the torque converter toward the trans. Some mechanics tie it to the transmission as they separate the engine from the trans.
Before you remove the fuel line or a return line, find a good plug the size of the line to plug each line or get a couple of fuel line clamp-offs if the flex lines are not hard and brittle.
A wise move is to get several containers and label them as to location on the engine. I usually use two just for the engine removal. One for everything I removed from under the car and one for everything on top. On a car with a lot of stuff to remove I use more containers labeling them "Right Side" and "Left Side". It makes putting the engine back in much easier. On the engine I use containers for different parts of the engine. On a V-8 or V-6 I use "Right Head", "Left Head", "front", "Rear", "Pan" but I don't mix inside the block with anything outside the block. On some engines they use grade "8" bolts to hold a cam sprocket on that look just like some outside bolts. Most bolts are marked on the head but many inside bolts are not. So never mix inside bolts with outside bolts.
Remove the head/s first. If it is overhead cam you will first need to remove cam belt if it is a belt drive. If it is chain driven cam/s you will need to refer to the service manual to find the procedure. Some remove the cam sprocket from the camshaft with the chain intact while others remove a "master link" from the chain and disconnect the chain. If it is a overhead valve engine you will need to remove the valve cover/s and remove the rockers. If the rockers are individual you should box them in the order they came out. If they are on a common shaft you will only need to do that when you disassemble the rockers from the shaft. It is important to keep the pushrods in order also. I found a good way to do this is to get a piece of heavy cardboard about a foot long and about 6 to 8 inches wide. Fold it so it looks like a foot long tent. Mark off the number of pushrods evenly spaced down one side and fold it together and drill about a 3/8" hole through both sides at each mark. With a marking pen mark which end is front. Spread the cardboard out like a tent again and push each pushrod in it's respective hole. Unless you have a lot of shelf space you can put a hole at one end and hang it on a nail or peg board to get it out of the way.
Some engines will drop the lifters out if you just pull a pushrod out. I found on these you should first lift the pushrod up slightly and move it hard side to side to release a lifter.
I like to remove head bolts in the opposite order that they are torqued. (refer to you manual) Many heads are stuck to the block and need to be forced off. On some engines this can be very difficult. Avoid the temptation to pry between the head and the block especially if the head is aluminum. If the head bolts were studs with nuts instead of bolts, double nut the stud and remove the studs.
If you are not familiar with "double nut", it means put two nuts on the stud and tighten them against each other (not against the head) then use the lower nut to undo the stud from the block. Then find a place at either end of the head to pry a corner or end of the head up. (Keeping away from the head to block joint)
I have seen many unique ways mechanics have used to brake a head loose from a block. Some engines are notorious for this. The 6 cylinder Jaguar was one of these. It was common to see a chain bolted to the head while the engine was still in the car and an engine hoist used to apply pressure to brake the head loose. I seen a mechanic lift the front wheels off of the floor on an E-Type to get it to brake loose and it still would not come loose so the mechanic left it hanging at the end of the day. The next morning it had come loose. One mechanic put the piston of #1 cylinder up on compression and put a half a cup of oil in the plug hole and replaced the plug and turned the crank with a long wrench on the front crank pulley. This worked but made a mess. Another mechanic in the same shop seen this and decided to rush the job by hitting the starter with a cup of oil in the cylinder. It broke the head loose but also bent a rod. I usually apply pressure like the engine hoist at one end of the head and find a lug or some sturdy part of the head to pry on. This usually works for me.