If invited to photograph a private event, be sure to visit the location beforehand to explore the options available and hence make plans for equipment and particular images that may be required.
Private events are often, although not always, held indoors - this presents an immediate challenge for a photographer in terms of low light levels. The good news is that digital cameras perform better than their traditional film counterparts in poor light, so life is nowhere near as difficult as it might have been in the recent past. The first priority for photography of this nature is therefore to acquire a DSLR, preferably equipped with a full-frame sensor, with a low-noise high ISO performance. A good professional zoom lens, perhaps 17 - 35mm or 70 - 200mm, featuring image stabilization and a wide maximum aperture is also a valuable asset. Where there is limited light intensity it is important to make best use of what is available - it is as simple as that.
Modern DSLRs make it possible to work at ISO 2,000, 3,200, or even 6,400 without unacceptable noise. The noise level inevitably increases as the ISO setting is increased, but a good noise filter can be used later to reduce any visible problems. A lens with a maximum aperture of f/2 delivers twice as much light to a sensor as one with a maximum of f/2.8, and hence the use of a faster shutter speed. It is important to know your equipment and choose the best basic settings. Select a shutter speed that is fast enough to obtain sharp pictures and an ISO setting that does not introduce unnecessary noise levels. The widest available aperture is often an acceptable choice, so a fast is always preferable.
The next problem to address is that of colour temperature. Indoor lighting may be supplied by tungsten or fluorescent sources, or some other mixture, perhaps combined with daylight from windows. The colour temperature may well be quite different in various parts of the same room. The best approach may be to use auto white balance and be prepared to make adjustments later. Shooting in RAW mode helps in this respect. Another approach is to take the time to experiment with various manual white balance and once again make any necessary changes at a later stage.
Exposure can be a real challenge in a room where lighting varies from one extreme to the other. near windows the light may be highly directional but reasonably bright. In shady corners the light intensity may be very low. Flash may offer a solution where it can be used, but in some circumstances it may be unwanted or the room may be too large to light evenly. Small on-camera flash units are of relatively low power and the the best option may be to turn them off. Larger flashguns are much more powerful and can be used to bounce light from white ceilings etc.
When using a zoom or telephoto lens, the amount of light reaching the sensor decreases as the subject is framed tighter. If a shot proves difficult because of lack of light, try to capture the same subject with a wide-angle lens so that a slower shutter speed is acceptable. Motion is generally less noticeable in wide-angle shots.
With all the low-light considerations under control, it is important to gain a proper understanding of what images are required. If you have been asked to photograph a particular event, make sure that a basic list of shots is agreed well before the event begins. If you are a guest, and taking photographs to provide a general record of an event, it may be left to you to decide how best to capture the proceedings.
Always remember that you are on private property and take care to respect the surroundings. Photographers who rearrange the furniture or stand on chairs without seeking agreement may soon fall out of favour. Similarly, it is at least a courtesy to ask whether the use of flash is acceptable. Someone in the room may have a problem of which you are unaware.
When photographing indoor events it may also be possible to venture outside, perhaps in to a garden or other open area. This immediately improves the light intensity, and may therefore be the best way to obtain an acceptable background and environment for portraits and group shots. Wedding photographers use a similar technique for exactly the same reasons.
Finally, remember that images of private events may not be published without specific permission.