Painting an engine and the engine compartment is a pretty fiddly process which, if done by a shop, can become quite expensive and if done by yourself, is patience taking to say the least.
The first thing that you will need to do is to paint all of the front end components. In most cases these parts are black semi gloss and they can be detailed with a good quality spray bomb. A quick caution here. If you are using spray bombs for any of your detailing you will have to remember that the paint comes out of them a lot thinner than a gun. For that reason you have to build up quite a few more coats than you would do with a spray gun. With a gun the worry is that the paint will be on too thick which can be a problem on mechanical parts. With the bombs just a couple of coats will give you no real depth and the paint will wear off and chip away very quickly, meaning a lot of touching up down the line. You should likely put on about six coats to get adequate coverage and durability. Don't try to compensate for the paint's thinness by trying to do it all in one spray. If you rush too much runs will be inevitable. Let each coat tack up before you apply the next. Often the time between coats will be given by the manufacturer.
Aside from black semi gloss paint for the front end components, you will also have quite a few other things under the hood that will go black. If you are lucky the firewall will go black but many manufacturers paint the firewall body color. In some rare cases the inner fenders will also be body color. If this is the case then you will need to take a trip to the paint shop to have all of the body color work done. If you have lots of black and want a good deep rich finish then that should also be done by the paint shop after you or they have done any repairs and prep work required to make the job paint ready. Extra holes should be welded up, dents repaired and any fitting should be done before paint. Fitting is pretty important as far as inner fenders and the front cradles and supports are concerned because if the car has had an accident in its past you may find things not fitting well during assembly. Sometimes old damage can be overlooked when an engine compartment is a greasy ball of dirt. When all the bits are fresh and new looking anything untoward will leap into focus.
Postwar cars often had quite drab engine compartments with the engines being painted rather dull colors, complemented with either gloss or semi gloss black paint and quite a bit of natural, cadmium plated or coated metal. The thing is that if you are going to show a car, all of these have to be faithfully reproduced which means firstly that you have to be quite sure what colors are on what. You may have removed a painted brake booster from your car but that could easily be a rebuild from days gone by. It may have been originally cadmium plated or some other rust preventative coating. Painting it will usually raise eyebrows with those who know, if originality is what you are shooting for.
Don't be put off by this however. You probably won't have to go running all over looking for places to get various parts plated and anodized and whatever else lurked below the hood. There are now, from suppliers like Eastwood and Bill Hirsch in the States, detailing paints that reproduce the look of natural aluminum, cast iron, cadmium plating and most other special coatings. Some of these, like the cad plate, are multi coat applications which come in kits of four or five different colors which when properly applied are indistinguishable from the original. Some like the cast paints not only reproduce the color of cast perfectly, they are also high heat so can be used very effectively to coat exhaust manifolds which normally rust very quickly after detailing. If you are painting the manifolds with high heat paint make sure to follow the instructions. Some need heat to cure properly so will have to be applied very close to your first start up, while other air dry quite effectively. In either case make sure you get a good build up of paint or you will get some rust coming through even with the paint. The color of your engine is, with show cars, critical. Manufacturers used to change engine colors quite often in the sixties and the right color will be critical to getting you a trophy.
Many of these colors are available from the same suppliers from whom you can get the other specialty products. Colors used by Ford, Cadillac, Chev, Dodge and others are commonly available and are accurate reproductions of the original colors. There are other paints which are listed for several manufacturers such as a green which is for use on Studebakers, Packards and others.
Although not absolutely exact in some cases, they are close enough to be acceptable in almost all situations. If you cannot get the color of your motor from a supplier or you do not want to use spray bombs on your motor then you will have to have paint custom mixed and sprayed by a paint shop. If you notice I don't advise you to shoot paint yourself, because unless you have a proper spray booth, fresh air systems and other equipment, you cannot shoot the urethane paints legally or safely, and it is urethane paints that you should use if you want the durability to put up with heat, oil and gasoline under the hood.
When you are painting your motor it needs to be stripped down as far as possible. One thing that both the educated public and judges look for under a hood is paint on gaskets. If an engine is painted without disassembling it, the gaskets will inevitably get painted along with everything else. To make sure that this doesn't happen you will have to remove your valve heads, water pump, timing chain cover, oil pan and almost everything else on the motor. This means that you will have to get a full gasket set including head gaskets. When painting the motor make sure that all of the gasketed surfaces are masked with tape and clean them of any overspray or paint that gets on them before reassembling the motor.
Once everything is properly painted comes the moment to put it all back together again.
Now cleanliness and good paint are all well and good but they won't do you a lot of good if you do not have the correct hardware on the motor. When detailing a motor you will have to use original hose clamps, nuts and bolts, wire ties and wiring. Make sure that the ignition wire set is a correct color and gauge and that the spark plugs are correct for the period. You may look a little foolish if you open the hood and reveal a set of Japanese N.G.K. or German Bosch plugs rather than Champions or another American plug. Special note here. Yes, some prewar cars ran Bosch plugs and electrical equipment, but those are the exception, not the rule.
You must make every effort to keep everything under the hood as original as possible. If you are using modern bolts because you can't reuse old ones or find older styles, you can file the markings off which will usually suffice, as few original bolts had much in the way of markings on them. Wiring harnesses were often tape wrapped or had fabric sleeves on them. The sleeves are available and you can still get wrapping tape at your local jobber. (Wrapping tape is just electrical tape without the glue). Don't get tempted to use the modern plastic ribbed wire covers as they are glaringly incorrect.
When you are finished assembling the engine compartment you can apply whatever decals or tags which may be available for your make of car. In some cases even reproduction inspection tags are available for some cars, but I have often thought them just a little silly as the customer never saw those as they were usually removed by the dealer.
Some even detail to the point of reproducing factory chalk marks under the hood and on the firewall. This is often found in muscle car detailing and on cars like Corvettes. Don't try it with a Packard.
Decals such as warnings, fluid levels and air cleaner badges are an important part of show detailing. Don't get tempted to put on too many though. Find out what was actually used and use only those. In some cases there are many decals available for a car which were used on different engines or option packages. Don't make the mistake of applying too many decals and under hood markings.
Although under hood detailing is time and money consuming as well as finicky, there is nothing quite as satisfying as lifting the hood on a car to reveal a better than new engine bay. I don't think that there is any one thing on a car that impresses quite as much as a perfectly detailed engine so it just might be worth the time and money to do it right.