If your chain had regular oil lube, or the lube that comes with a new chain, it's nice to have some latex gloves to handle your dirty chain. If you were using wax on your chain, it isn't too bad without gloves.
To take the chain off the bicycle, you will need one of two tools, depending on if your chain has a master link, or not. If your chain has a master link, it's much easier to get it off with a tool such as the Park MLP Chain Plier. Otherwise, you will need a standard chain removal tool: http://google.com/search?q=chain+removal+tool&tbm=isch
Some Shimano chains are directional, and require you to work with a certain connecting pin in only one direction. See example: https://www.youtube.com/watch?v=Ufm19cvrxGs I didn't use a new pin on my 11 speed chain, as required by Shimano, and was really careful to recenter the old pin. So far so good, but you might want to read on other people's experiences. Maybe I will someday. However, I did read, that on an old chain, replacing with a new pin causes problems, because the chain link possessing the new pin, will be shorter than the other links.
You can use mineral spirits, or kerosene, or paint thinner, to clean your chain. Mineral spirits evaporates quickly, so you won't have to wait long for the chain to dry. Pour enough into a plastic bottle with a large mouth to submerge the chain. Seal the bottle with the solvent and chain, then shake violently. Allow to soak, then repeat. Let sit again for the sediment to settle to the bottom. Use a tool to take the chain out of the bottle (I use a J-bend spoke for this). Your chain will look shiny new.
There are two schools of thought, regarding chain lubrication.
One is that you need a wet lube to keep the surfaces of the chain coated with lubricant. The downside, is that wet lubricant attracts dirt. This could have the effect of creating a lube bath with grit. The grit in the interior of the chain will wear the chain faster.
The other school of thought, is that you can use a dry lube. Detractors of dry lube, say that since it is not wet, it doesn't stay in place, and gets pushed off the chain surface, especially with the shear forces occuring in multiple speed drivetrains. However, dry lube does not attract dirt. Some dry lubes are semi-wet, and are a trade-off between wet and dry lubes.
Chain wax is one type of dry lube which can theoretically waterproof and create a seal through which dirt can't enter. Another benefit, is that a waxed chain won't leave big black stains on your hands or clothes, and the chain looks shiny for a long time.
Wet Lube: Any synthetic oil will do. Your drivetrain will require frequent maintenance to look clean. Since most people don't do frequent maintenance, it ends up looking dirty rather quickly.
Semi Dry Lube: Rock and Roll brand Gold lubricant. This is a semi-wet wax and/or/maybe ptfe in solvent. It attracts less dirt than wet lube. Still need to apply frequently, in order to keep the chain lubricated, and since it applies with solvent, you are also cleaning the chain in the process (by applying a lot and wiping with a rag).
DIY Chain Wax:
85% paraffin wax
1% ptfe powder
It doesn't add up to 100 percent, because it is not a precise science. I've used a pre-made chain wax I would buy in a can in the 1990's. I loved it. I can't find the brand anymore. It would wash off after multiple rain storms, and I knew it was time to redo the chain when I heard squeaky noises. Usually not at the most convenient time to take the chain off the bicycle, and make a chain wax pot roast on the kitchen stove. I plan to return to using chain wax, and have multiple chains, so I can change out the chain for one that is ready to go. That way, I can re-wax the used chain at a later time.
Place chain into melted chain wax, and give a few minutes for the wax to penetrate the chain. Pull hot chain out with a tool and leave to cool. After the chain cools, work the links loose and rub off, or blow, the wax shavings that result.
Note: “Most paraffin waxes have a flash point around 390° F. When it reaches its flash point it may not smoke or bubble, it will usually just explode, splattering flaming wax in all directions. To avoid this dangerous catastrophe, always use the double boiling method to melt your wax. Water boils at 212° F, which is well below the flash point of any paraffin wax.”
If you make your own, and buy in bulk, you will be paying at most $3 to $4 per one pound chain wax. Compare with $16 for a half pound. I am curious to try Squirt Lube, which is an emulsion of water and a few waxes.