Filters basically break down into two categories. Visual filters and Imaging filters.
Visual filters are usually some color, very similar to camera filters. They are used to enhance the color of objects, like planets. You see the object, and you'll use a filter to add contrast. Since most of the observing you'll be doing that a filter will have an effect on is going to be planetary or lunar, here's a great article on the basics of VISUAL filters.
Astroimaging filters are far different. Since a camera can have a much longer exposure time than the human eye, it can 'perceive' dimmer objects, and also can perceive wavelengths beyond our own capability, such as ultraviolet and infrared.
The intent of ALL filters is to block some wavelength of light. So, if you have a 'red' filter, you simply have a piece of glass that is coated in such a way that it blocks all wavelengths except the red part of the spectrum. A blue filter blocks all the wavelengths except the blue. Then, you'll have polarizing filters, which are two filters with special coatings on them that block out a percentage of the light. A Variable Polarizing filter allows you to change how much light gets blocked out. Variable polarizers are great for the moon, since you can cut back on the amount of light to your eye.
For imaging, you have a basic 'LRGB', or Luminence, Red, Green and Blue filter set. The RGB set is very basic, in that those three colors can duplicate our visual spectrum. Red, Green and Blue make up every color we can see, and when combined, produces white. Yeah, I know that sounds a bit strange, but take my word for it, okay? It's not the filters themselves, but the combination of those three spectra of light that do it. This is where the 'Luminence' comes in, it provides for the 'white', in the most basic of concepts. The LRGB color set is used with monochrome imagers, or devices that can not recognize color. Color sensors, like in a DSLR, has something called a Bayer Mask over it. It's a matrix two pixels by two pixels, where two of the pixels are green, and then one each for red and blue. This mask or matrix over the sensor is how the camera 'sees' color and recreates it.
Then, there are specialized imaging filters, the three most popular are Ha, or Hydrogen Alpha, OIII, or Oxygen III, and SII, or Sulfur II. Each of these filters allows only a very narrow part of the visible light spectrum to pass. Here's Astronomik's page on their 'Narrowband' filters.
You would not use these filters for visual use. First of all, the targets they are designed for are usually faint fuzzies, and secondly, they would remove all of the visible light except for the band of spectra that they are designed for.
By the way, these narrow band filters are also used for monochrome cameras.
You didn't specify what you wanted filters for, but I'm assuming visual. You'll also hear about 'nebula filters' and 'light pollution filters' and those again, fall into the imaging category, not the visual category.
For visual, you might consider this set of 6 filters.
For Lunar stuff, I recommend a variable ND, or Neutral Density filter. This allows you to change the amount of light, anywhere from 5-25% of the incoming light. In and of themselves, ND filters usually require the removal of the eyepiece, and changing out the filter on the bottom of the eyepiece and then reinserting it. With non-variable ND filters, you need to have one for each transmission level you want, so it makes it more expensive in the long run. There are variable ND cells that allow you to change the density of the filter, but require you again remove the eyepiece from the diagonal.
Meade, and BST, both have variable ND filters that you put the eyepiece into, and then adjust the filter without remove the EP.
I hope this answers some of your questions.