Power supplies look intimidating at first glance. Numerous connections spew from them like demonic spaghetti, and each strand ends with a specific connector. To the untrained eye, the various kinds of connections can be hard to figure out - but they're easier to understand than they seem.
I Bought A Power Supply. It Has Pasta Dangling From It.
Power supplies, even new ones with special sleeves designed to make cable management easy and more attractive, are far from the most graceful products in the world, or the least confusing. Video cards, processors, and hard disks tend to come with details instructions detailing exactly how to proceed with installation, or at least have them online. But buying a power supply generally nets you only a thin warning about the dangers of working with a power supply when it is plugged in, and a little baggie with four screws.
Making sense of the plethora of connections is, therefor, often difficult. Sure, certain pieces seem to sit properly in certain places, but this is a power supply we're talking about. Best to err on the side of caution. But don't worry any longer, because this quick guide details all the different connections you might find on a modern power supply. In practice, most connections do more-or-less fit where and only where they're supposed to, but since this isn't Lego blocks we're hooking together here, a bit of reassurance doesn't hurt.
Molex Connections
More likely than not, most of the dangley bits hanging from your power supply are going to be Molex connections. A Molex connection is a flat, rectangular four-pin connector, with two angled corners so that it will only fit one way. Typically, it will have four wires coming from it. The plastic end of the connector can be any color, and it usually is not printed with any sort 
of label. Most Molex connectors are kept in place only by friction, which is to say you have to give them a good shove in order to get a male and female end together, and give a good tug (on the connector, never pull on the wires) to get them apart.
Molex connections are very common because they are used to power all sorts of accessories, like case fans, some internal and external drives, and any special features like customized lighting. They can sometimes be difficult to use because they are only kept together by friction. Most Molex connectors are the standard four-pin design, but you may also run into some specialty connectors. For example, some companies use "Fan-Only" connections which look like standard Molex connections, but which only have two pins.
SATA Connections
The SATA power connection is meant primarily for internal and external drives, and replaces some of the function of the Molex 
connection, which used to be the primary power connection for hard drives and external media drives. It is still rectangular, but is much thinner than a Molex connector. It also has an L-shaped connection, which ensures that the connector can only be inserted in a particular fashion.
There are adapters which can turn an SATA connection into a Molex connection, or vice versa. Most power supply only include four or five SATA connections, because they are used only for hard drives and external media drives. This means a Molex-to-SATA adapter may be required if you have numerous SATA drives, or an older power supply.
4-Pin Or 8-Pin 12V Motherboard Connection
The 4-pin motherboard connection is probably one of the most confusing power connections around. The area it connects to on a motherboard is not intuitive to those who have not constructed many computers. However, the shape of the 4-Pin motherboard connector is unique, both because of its 2x2 pin design and the shape of its pins.
The purpose of this connection is to provide power to the CPU. In some rare instances, mostly involving ancient motherboards and/or processors, this may not need to be plugged in. However, most modern machines will require it. This connection can be difficult to plug in, but it is designed to only fit one way, because aligning the prongs wrong could cause damage to your computer. A visual inspection of the connector should allow you to line up the connection properly. Most 4-Pin motherboard connectors keep themselves secure with a latch, and are easy to attach and detach because of this.
In some instances, when using motherboards that support multiple CPUs, you may run across an 8-pin connection. Not all motherboards which have the potential to accept an 8-pin connections need an 8-pin connection. Some will accept the 4-pin connection. There may be drawbacks to using only a the 4-pin connection, however, so consult your motherboard manual.