Beyond the obvious of using appropriate equipment, I'll go over a few other tips which can help one ride safer and more enjoyably. The most important safety rule to remember for both recreational and commuting riding is to be fully aware of your surroundings. No safety equipment will be as effective at keeping oneself out of harms way beforehand. In addition to keeping aware of your surroundings, being visible is also an important part of staying safe, as others cannot avoid and take into account ones actions if they cannot see them.
There are quite a few things which can be done to improve one's visibility, especially if one is riding near car traffic and/or if one is riding in the dark.
Your standard safety vest. As visibility is important, an wearing an eye-catching color (in this case construction worker yellow) as well as retroreflectors to reflect light in low-light conditions is as basic as it gets. If the design puts you off, there are retroreflective vests styled for biking and any number of aesthetic tastes. Just remember, it's better to look stupid than look dead.
As for the bike itself, it is recommended to add either lights or retroreflective tape to the body of the bike in such a way that all viewing angles have at least some visibility directly towards the retroreflective portions, if using retroreflectors, or light-emitting portions in the case of lights. Moreover, the lights and/or retroreflectors should also cover up to the maximum extents of the bike, including the wheels if possible.
Front and back retroreflectors. It is generally preferred to use lights, but having a set of retroreflectors as backup in case your lights go out is a good idea.
Headlights and tailights are essential not only for low light conditions, but also for general visibility, as they can broadcast your presence further than an absent-minded driver will normally spot.
Similar to my advice regarding retroreflective tape, LED lighting is another popular way of increasing visibility on ones bike. the drawback to LED lighting versus retroreflective tape is, in the end, down to weight and battery life. There are also in-wheel lighting options which utilize the kinetic energy of your wheels in motion to generate light.
Impact and Riding Gear
This is the stuff you buy and hope never actually gets used. Helmets, pads, gloves, eyewear, etc. The last line of defense if visibility and awareness fails.
The helmet is a pretty standard and pretty self-explanatory piece of impact gear. There are many styles of riding helmet to choose from, ranging from standard race styles to skateboard style helmets and even full-face dirt bike helmets.
Pads are a much less common piece of gear, but if you're a beginner, you'll probably be glad on more than one occasion for wearing them. Also a self-explanatory piece of gear, there are also many different styles to chose from, but most will suffice for blunting an impact or preventing serious abrasion.