A church is often a dark environment, especially if it dates from the Middle Ages. This means slow shutter speeds and a high risk of blurred images when you take no action.
If it is allowed to use a tripod, make sure that you use the lowest possible ISO (not lower than standard, so no “Low” setting) and an aperture around f / 8 and f/11 in order to get sufficient depth of field in the picture. Ideally would be using a remote control so you do not have to touch the shutter button (this can cause unwanted vibrations). You can also consider shooting with a monopod.
When it isn’t allowed to use a tripod, you can still come home with great photos, if you take into account the shutter speed and use the capabilities of your camera. Try to keep on to a minimum shutter speed similar to the focal length of the lens. Shooting at 100mm, keep 1/100s as minimum shutter speed, shooting on 50mm than 1/50s, etc. Generally many people can hand hold their camera up to 1/30s, sometimes stretchable to 1/15s . It helps if your lens or camera has image stabilization.
The easiest way to speed up the shutter is to open the aperture (a lower f-number such as f / 4 or f/2.8) so more light can fall on the sensor, but often this will not be enough to hold the camera steady in the hand.
When it is desirable to use a poet apperture (higher f-number such as f / 8 or f/11) to achieve a greater depth you can raise the ISO so that the sensor is more sensitive to the light that falls on it, often the colors even get more brighter, which can give a nice effect with stained-glass windows.
However, this has the disadvantage that there arises more noise in the picture, which if it gets too bad, could destroy the finer details.
The church itself is quite dark, but often there is a lot of light through the high windows. When you want both the inside of the church, and the windows to put in the picture, you run into the limitation of the dynamic range of a camera sensor. This can distinguish less light than the human eye, which – depending on where you measure the exposure – causes the windows to lose all the details and become white, or the interior is no longer visible in the dark black shadows.
One way to prevent this is to take your photos with different exposures using the bracketing function of the camera. This automatically takes a photo at -2, 0, or +2 or -1, 0 and +1, at home you can merge this photos with for example Photoshop or Photomatix Pro so you can see both the details in the dark areas as the details in the light areas.
You can also stabilize your camera on church benches or hold pressed against a pillar. Especially in churches with Gothic architecture, there are a lot of places to hold the camera steady. Do not forget to use the ground, this offers a low position to emphasize the size of the church with an extra wide.
One trick that often works is to keep the shutter button pressed down longer, so more pictures are shot in sequence. In a set of 3 to 5 photos there often is a sharp picture. Otherwise let yourself be guided by the light, look at the places where the light falls, so you see/know where you can get relatively fast shutter speeds.
The winter months are a great time to visit a church and to photograph it. Not only is it less busy in the churches that are popular among tourists, but than the sunlight is lower, causing that also the ceiling gets exposed. But actually, you can always shoot in a church, observe the light in different parts, you can often find a composition where the light is beautiful.