Coaxial speakers (or three-ways) are two (or more) speakers built-in the same frame. They are cheaper than separate woofer and tweeters and also easier to install. There is no need to worry about crossovers, since they are already built-in (you might still need to add a crossover to block bass if you are using high-power amplifiers). A disadvantage of coaxial is the lack of flexibility. For example, if the coaxial is all the way in the kick panel, or door panel aiming at your feet, not your ears. Some manufacturers try to compensate for this by making adjustable tweeters. You should usually consider coaxial speakers for the back of the car, in a car audio installation, and separates for the front, unless you only have one speaker hole and don't plan to cut any more holes in the car, for the audio installation.
Separates consist of a tweeter and woofer, and [most of the time] come with an external crossover. The woofer is usually mounted in the factory hole in the door or kick panel. The tweeters can be mounted in different places. The most common place to install tweeters is towards the top front corner of the door panel, aiming (if possible) between both front seat head rests. Another popular location for tweeters is in the dash, either surface mounted, or in factory dash holes. Yet another location where tweeters are commonly mounted is in the blank plastic piece on the top front side of the doors (where the mirror is on the outside). You would have to experiment with angle and location to achieve the best possible imaging and staging.
Midbass are usually 5, 6 or 8 inch speakers that are designed to go lower in frequency and are part of a three way system with a mid and tweeter. The problem is that 3-way arrangements require more complicated crossovers. A well-balanced three-way set up will give you accurate imaging and staging. Midbass are most commonly mounted in the doors.
Subwoofers add lower frequencies to the whole system. They have to be enclosed in a box, with the exception of free air subwoofers, which use the trunk as a box. There are many different types of boxes and implementations discussed in the subwoofers section.
A few high-end manufacturers are making horns for car audio use. Horns are very good at directing sound and have high efficiencies. Horns are usually mounted under the dash. By doing this, difference in distance from left and right speakers are greatly reduced over conventional mounting locations. Since horns play mids and highs, tweeters are not needed. Even though horns are mounted under the dash, they give great imaging. Horns cost more than conventional speakers and require customization. In many installations a good equalizer is required to compensate for their high sensitivity.
Center channels consist of a midrange speaker (3 or 4 inch) mounted in the middle of the dash (usually) on the top. Center channels play a mono (Left + Right) signal between 350 - 500 and 3500 Hertz (voice range). The purpose of the center channel is to raise the sound stage, by creating the sensation of the singers "being" in the front of the car, in a car audio installation, and not in the door panels. Center channels are hard to implement though: First, a band pass crossover is needed. Left and right channels have to be summed up. There are various commercially available center-channel processors (many with built-in amplification). The volume level of the center channel should be lower than the other speakers, since it is only supposed to make subtle changes to the total sound image