The Webster entry for pipette is correct as far as it goes, but there have been a few advances since 1913.
Common types of pipettes include the following:
The volumetric pipette is the one referred to by the Webster definition. Common sizes range from 1/2 milliliter to 100 mL. They also come in a range of accuracies. Those used in a college lab might not have a certified tolerance, or will be class B. In a laboratory required to follow Good Manufacturing Practices/Good Laboratory Practices such as a quality control lab at a pharmaceutical company will generally use the more expensive class A volumetric pipettes. These have tolerances ranging from 0.006 mL for a 1 mL pipette to 0.08 mL for a 100 mL pipette, and can cost more than $30 US each. Volumetric pipettes can be further subdivided into the categories of To Contain (TC) and To Deliver (TD). A TC pipette has a graduation mark indicating where to fill it such that it contains exactly the stated volume, implying that all of the liquid must be ejected from the pipette in order to transfer the exact amount. A TD pipette is graduated such that when filled to the line and allowed to drain, the exact volume will be delivered leaving a small amount of liquid in the tip of the pipette. A class A TD pipette will deliver its certified volume of water at 20oC in twenty seconds. The volume delivered will not be accurate if the liquid being measured does not have the same surface tension properties as water, since a slightly different volume will remain in the tip. This difference is usually negligible, but for critical applications it is best to use a TC pipette and quantitatively transfer the solution.
Use of a volumetric pipette is a bit of an art, and everyone develops their own style. The basic concept is that suction is used to pull liquid into the tube to a point above the graduation, the level of liquid is carefully brought down so that the meniscus is at at the graduation mark, then the liquid is drained into the container it is being transfered to. Originally, the chemist/biologist/etc. would "mouth pipette", that is, they would use their mouth to suck the liquid into the tube. For obvious reasons of safety this practice has become all but extinct. The only time I've ever seen it done was in the movie Strange Brew by Brewmeister Smith. I've heard stories about people in crime labs accidentally sucking solutions of illegal drugs into their mouths using this technique, but that is as hard for me to comprehend as the fact that people used to smoke in laboratories.
The most common method is to use a rubber bulb to pull the liquid into the tube. Once the liquid is above the graduation mark, the bulb is removed and a finger or thumb is used to cover the opening to prevent the liquid from draining. The tip of the pipette is then wiped with a lint-free tissue to remove residual liquid from the outside of the glass. The finger covering the top of the tube is partially (and very carefully) raised so that the liquid slowly drains down to the graduation mark, then full pressure is reapplied. This operation is usually performed with the tip of the pipette touching the side of the original container so that a drop isn't left hanging from the tip. The tip of the pipette is then placed in the container the liquid is to be transfered to and allowed to drain. If it is a TD pipette, its tip should be carefully touched to the side of the container or the surface of the transfered liquid to allow surface tension to pull the correct amount out of the pipette, leaving a small amount of liquid inside. Once a TC pipette has drained, a rubber bulb can be used to force the remaining solution out of the tip, or alternatively, a solvent can be rinse through the pipette from the top to remove the original sample in its entirety.
Very often it is necessary to wear gloves while pipetting, making it difficult to control the level of the liquid using a finger or thumb. In some cases the analyst can safely cut the glove to expose the finger or thumb, but usually this will make the use of gloves pretty pointless. For these situations the analyst can use a safety bulb. This is a rubber bulb with one end that goes over the pipette and a side-arm between the end and the bulb itself. It has valves that are opened by squeezing them. The analyst opens the valve above the bulb and squeezes the bulb to remove the air, then closes the valve. The valve above the pipette is then opened, allowing liquid to be sucked into the pipette. The valve on the side-arm is then opened to allow the liquid to drain.
The graduated pipette operates using the same principle as the volumetric pipette, but as its name implies, has many graduations instead of being intended for measuring a single volume. This flexibility comes at the cost of reduced accuracy.
The pasteur pipette is really just a disposable eye dropper. It is a glass tube with a tapered end typically 5 1/2 or 9 inches in length. A rubber bulb is attached to the large end to make it work, although capillary action can be used to draw liquid into the tip. A transfer pipette is disposable plastic tube with an integrated bulb at top. These types of pipette are not used for exact measurements
The auto-pipette is what is described in quincyfree's write-up, although I've seen volumes up to 10 mL, and they usually cost hundreds of dollars (for good ones anyway). They can be fixed volume or adjustable, but as with volumetric vs. graduated pipettes, the flexibility of a range of possible volumes comes at the cost of reduced accuracy when compared to a fixed volume pipette. Technique is very important when using an auto-pipette. The basic operation is to place a diposable plastic tip on the end of the contraption, press the button on top to move the piston down, place the tip in the liquid to be transfered, release the button so that the piston returns to its starting point drawing liquid into the tip, place the pipettor over the container the liquid is to be transfered to, and finally press the button down to force the liquid out. The analyst must become familiar with the "feel" of each auto-pipette, which means recognizing when the piston has been pressed down all the way. Most have one distance you press the button to before drawing in liquid, with a second position the button is pressed to when ejecting the sample. Auto-pipettes are typically calibrated by delivering volumes of water at a known temperature into a container on a balance. Because the density of water is well characterized over a wide range of temperatures, it is possible to check whether the weight of water actually delivered matches the theoretical weight for the volume the pipettor is supposed to measure. Multiple measurements are usually taken, and a good pipette/analyst combination should be able to achieve a percent relative standard deviation of 1% or less for 5 to 10 measurements. As with volumetric pipettes, accuracy decreases as the volume measured decreases. Because of the mechanical nature of auto-pipettes, calibration checks need to be performed often to ensure they are still delivering accurate volumes. Quincyfree described the practice of touching the tip of the pipettor after delivery to remove the remaining liquid, but this should only be done if that was the technique used to calibrate the pipette. Auto pipettes are rarely as accurate as a good analyst using volumetric glassware, and consequently should not be used for critical applications despite the tremendous savings in time the use of an auto-pipette can provide.However, as belgand has reminded me, an auto-pipette is really the only realistic choice for very small (microliter) volumes.