I've done quite a bit of this - it's fun and not at all difficult. There are a number of books out there, but in my opinion, most take you further than you probably want to go by discussing all kind of exotic techniques. Walk before you run - actually, I learned mainly by doing, although I did take a half-day workshop at a nearby arts center many years ago.
First concern: paper. Gay is absolutely right - you need a matte surface, and my experience is that fiber works FAR better than RC. I have always used ORWO, but my stock is very limited and can't be replenished. I bought a package of an Ilford matte-surface aftermarket paper, but I wasn't all that excited with the results. Kentmere is reported to have ome good papers for hand coloring, but I don't have any actual experience with them.
You can buy a dulling spray that supposedly allows you to hand color on glossy paper. Don't bother - it doesn't really work.
Second issue: I found that pencils were much easier to use than oils. I started with Marshall's pencils, but over time expanded my collection with a variety of artists pencils.
My method is to tape the print to a sheet of heavy cardboard. I use a smooth, white artists tape and apply it all the way around the print, completely masking the border. That makes it possible to have clean, white borders when I'm done.
The first step is to apply a thin application of Marshalls PMS solution - which appears to be a mixture of turpentine and linseed oil. I use a bit of cotton moistend in the solution, and simply wipe across the entire image, making sure to cover everything with a thin application. Emphasis on thin.
Then, starting in the middle of the print, I apply color by rubbing gently with the edge of a sharpened pencil. The tooth of the matte surface helps grind away a bit of the pencil, and the residual turp/oil mixture also dissolves the pencil to create a thin, transparent oil paint-like gel. I use cotton balls, "Q-tips", and even toothpicks wrapped in bits of cotton to rub this gel, ususally in a circular pattern, to smoothly color bits of the image. If desired, I can use multiple pencils and blend their colors to create an intermediate hue. The idea is to rub it smoothly into the surface of the paper - that means lots of rubbing.
The key is to use a circular motion, coming up to the edge of elements of the image. As additional colors are added to the image, the circular motion up to the edge will cause the colors to blend smoothly. The key is to practice.
I prefer subtle hints of color, perhaps even on only some elements of the image with the remainder left monochrome. I find that the PMS solution has a tendency to yellow as it dries, especially if it is applied too generously, but that can be managed by applying a very thin gray or white wash in areas that aren't to be colored.
It can take some time to apply pleasing color to a print - a 8x10 print could take an hour or more to color. After I'm done, I lay the print aside to dry while still taped to the cardboard. After it's dry, I gently remove the tape, being careful to always pull toward the edge of the print so that it doesn't tear the emulsion. CAUTION - drying is very slow. Allow three or four days, and a week is better.
Marshall's oils are also fairly easy to apply, but a bit of oil goes a very long way. That's why I really prefer pencils. And frankly, having to deal with those tiny lead tubes, that want to dry up so that the caps won't come off then next time you want to use them, it a PITA. On the other hand, using oils is convenient for a wash color for a large area.
I have also experiemented with conventional artists oils, mixed with a transparentizing gel. That works, but in the end I keep coming back to pencils as the most controllable approach.
If you have areas in the image where you want to completely remove color, Marshall's Marlene is perfect for that. For example, to brighten highlights in the eyes in portraits. Just be aware that it is generally not possible to apply another layer of color over an area where color has been removed using Marlene. Use it vary sparingly with cotton balls, Q-tips, and bits of cotton wrapped around toothpicks.