A front is one of the basic building blocks for the formation of clouds and precipitation in the atmosphere. A front is a boundary separating two air masses of differing densities and/or temperatures. There are several types of front - here are the main ones and what they look like on a weather chart: 
It is also possible for a front to form above the surface, called an upper-air front. Shear lines,                        and                  also exhibit some frontal features, but are not strictly fronts themselves. Typically, a front will be around 1000 km long and around 100 km wide - of course, fronts can come is many sizes and scales, but they are usually at least 10 times as long as they are wide. The warm front, cold front and occluded front affect us the most in the UK. Stationary fronts are less comman, but tend to occur more in the summer. 
A warm front gradually approaches with increasing cloud cover over a period of 12 - 24 hours. Some slow moving warm fronts show signs of their approach up to 36 hours before they arrive. Warm air is forced to rise over a cooler, more dense air mass, producing stratiform precipitation from stratus and nimbostratus clouds. The cloud base gradually lowers and rainfall steadily increases as the front approaches. 
squall lines
dry lines
Diagram of an approaching warm front. Cirrostratus is the first sign, with cloud gradully thickening and lowering as the front approaches. Rain or snow can fall, depending on the temperature at the surface. 
Credit: Meteorology Today textbook, by C. Ahrens
The front is the location at the surface where the warm air mass begins. Typically, the gradient of a warm front is 1 in 400 to 1 in 100, so the front will be in different locations at different heights. In the warm sector behind the front, shallow convective couds may form, or stratus may form if there is enough rising motion; producing some precipitation. Unlike a cold front, it is thought that a warm front propagates by mixing its way forward. This may explain why warm fronts generally move slower than cold fronts. 
A cold front does not usually show any sign of its approach - when its affects are felt at the surface, then the front has likely already passed through. This is because the clouds and precipation all occur behind the surface front, as the front tilts back with height. Typically, heavier precipitation occurs along this front, with convective clouds and thunderstorms possible. Cold fronts tend to have much stronger temperature gradients across them, accompanied by a significant change in the wind direction from south or south-west to north or northwest. 
Diagram of an approaching cold front. Cumulonimbus clouds can form because the front acts as a trigger mechanism for convection, unlike a warm front, which acts to "cap" the atmosphere. 
Credit: Meteorology Today textbook, by C. Ahrens
Stratiform precipitation from nimbostratus/ stratus clouds can also form behind the front if the atmosphere is stable. If the atmosphere is very unstable, a cold front can act as a focus for severe thunderstorm development, such as in the US in spring. A cold front will typically have a gradient of 1 in 100 to 1 in 40. Because the cold air is denser than the warm air ahead of it, it flows forward as a density current, essentially wedging under the warm air. In a mid-latitude cyclone, the cold front will eventually catch up with the warm front to produce an occluded front. 
An occluded front contains a mix of clouds and rainfall from both warm and cold fronts. When the cold front reaches the warm front, it undercuts it and lifts the warm front off the ground. When a cyclone becomes occluded, it means that it is likely weakening, since the surface temperature gradient that is crucial for storm developmet has weakened. At the surface, there is not generally much of a temperature change when an occluded front passes, although there may be a subtle change in the wind direction. 
Schematic of an occluded front. It takes on properties of a warm front - with cloud gradually lowering as it approaches, and a cold front - with convective clouds potentially forming behind it.
Generally, the cold front contains colder air than air ahead of the warm front, and so the occluded front looks like that in the diagram above. This is known as a cold occluded front and is most common. Occasionally however, the cold front may contain slightly warmer air than the air ahead of the warm front. In this situation, the cold front overrides the air ahead of the warm front, producing a warm occlusion. 
A stationary front is simply a stationary boundary between warm and cold air masses. They usually occur in a calm atmosphere where winds are relatively slack, but they act as a zone for cyclones to develop and move along. 
Within the front itself, it is important to note the flow of air relative to the movement of the frontal surface. This can impact the positioning of the cloud band and the intensity of the precipitation. In an Ana front, the warm air moves up the frontal surface, generating thick clouds and heavy precipitation. There is a greater potential for convective clouds in this case. In contrast, in a Kata front, the warm air moves down the frontal surface, supressing cloud formation. Any rain is likely to be light and the clouds will have lesss vertical extent.
Schematics of both an Ana and Kata cold front. The cloud band tends to be ahead of a Kata cold front, whereas it will be behind an Ana cold front.