In the winter, it can be hard to find a time to run in the few daylight hours that are available. You may also find yourself in a race that takes place in darkness. Either way, running in darkness brings its own challenges, both practical and psychological.
Practical issues - Lighting
One option for running in the dark is to stick to well lit paths. If you do this near cars, be sure you have plenty of reflective gear; runners nearly always do worse than cars when the two collide. I would also recommend a flashing yellow/red LED light attached to the back of your shorts. Something like this Nathan is cheap and works well - http://www.rei.com/product/785894.
If you are running away from street lights, then carrying your own light source becomes important. (You can run by the light of the moon sometimes, but I do not rely on it.) The most common approaches are headlights or hand held flashlights. The advantage of a hand held flashlight is the light source is lower than your eyes, so bumps in the path cast shadows you can see; this makes it far easier to see the shape of the path. The downside of hand held lights is that having something in your hand is a pain.
A nice solution to this is the Petzl Tactikka XP Adapt (http://www.rei.com/product/737855). This light clips to the waist of your shorts, providing a waist level light that is hands free. The other thing I like about this Petzl light is that it has a diffuser to create a nice even light that works really well. This is my preferred light for most night running. For early mornings it is doubly nice, as when the sun comes up, it is very unobtrusive. It is not recommended for use with lithium batteries, but I have done so without a problem. It does work with rechargeable batteries, but when the power runs out, it runs out fast! I have found that the light works well with compression shorts - I'm not sure how you would get on with something baggy.
For trail running in the dark, where I also want to see much further than the Tactikka, I have the Petzl MYO RXP, which is their first regulated headlight (http://www.petzl.com/us/outdoor/myo-series/myo-rxp). A regulated light stays at the same brightness until the battery in nearly flat, then drops very quickly. The RXP is much, much brighter than the Tactikka and without the diffuser in place, it will illuminate the trail for a good distance. This makes navigation much easier and reduces the sense of confinement you can get when running for a long time at night.
The combination of the Tactikka and the RXP works well for me. I wish there were a brighter version of the Tactikka, as the RXP tends to overwhelm its output.
Amongst my many other headlights, I have the Petzl MYO XP Belt, which has the batteries in a separate box that attaches on your belt (hence the name). It is a good idea for keeping the load on your head down, but the wire is very thick and inflexible, which annoys me. The wire has also broken on my battery pack, which is disappointing. It is a great light for extreme cold, as you can keep the batteries warm, but other than that, I would not recommend it. http://www.rei.com/product/770394
As you may have gathered, I like the Petzl range of lights. I've had other brands, but none work quite as well for me. The flip down diffuser that Petzl includes on many of their lights is invaluable. They are not waterproof, but I've never had a problem wearing one in heavy rain. Carrying one upside down around my wrist once caused some temporary problems though. I'd love to try the Petzl Ultra, but at $430, it is out of my price range. http://www.rei.com/product/786019
The only other safety tips for night running on remote trails is to carry a bear bell to help keep the creatures away and a cell phone to call for help, just in case.
There are a number of psychological issues with running in the dark. The biggest challenge for me running in the evening is that when the sun goes down, I want to go to bed. The feeling of sleepiness, particularly if you have been running for many hours can be overwhelming. I have overcome this, partly with practice, and partly with a different mindset. When I look at my watch and discover it is a particular time, I work to detach myself from the meaning of that time. If it is 10pm, I don't think 'I should be going to bed'. I work to imagine I am in a different country on a different time zone, and generally, it helps. Even on MMT, when I was racing for 34 hours, I did not suffer from sleepiness.
Another problem with running at night can be a sense of isolation. Your world can become a small circle of light, with no other points of reference. Running with others, or running near roads can reduce this sense of isolation. I find that the time just around sunset is the worst for me, as it combines with a sense that I should be tucked up in bed, not out running.
The darkness can lead to an irrational fear. Being scared of the dark is quite natural, especially if you are exhausted. I was told by an outdoor survival expert that the key is to have a 'predator mindset' not a 'prey mindset'. You have to believe you are the biggest, baddest thing out there. I found this advice really worked for me. Note: this deals with irrational fear, but some fears are rational and need to be dealt with differently. If there are reasons to be afraid of wildlife or people, you need to be equipped to deal with them or take other precautions. Pepper Spray (I usually carry some), bear bells, cell phones and most importantly, running with a friend can all help alleviate risk.
My remaining psychological issue is that I run much slower in the dark than the light. I always feel like I am running much faster than I actually am. Looking at my watch that displays pace helps compensate a little, but not completely.