I get this question often. My answer is always the same, find a reputable local investigator or group and connect with them. Take the basics, flashlight, first aid kit, and dress appropriately for where you are going. That is usually followed up by, "What investigative equipment should I take?" I recommend beginning with a basic camera. Unlike digital voice recorders which produce many false positives, EMF meters that may require learning some special skills, and other equipment that can get pricey, most already have a camera which can get reliable data if used correctly. This article addresses that issue.
One of the easiest ways to investigate and the method most use on their first few attempts is a camera. It requires little special skill, at least initially for the basic point and shoot type, and allows a newbie to determine if paranormal investigating is really something they want to get involved with. Regardless, it should be done correctly.
Though daytime investigating is preferable when possible most seem to want to go at night. I am assuming when writing this that as a newbie you are teamed up with one of those groups. Also note that I assume that as a new investigator you have only a basic camera. Consequently this article will not go into a lot of detail most veteran investigators and photographer know related to capturing evidence. I have condensed all of that down to the very basics; Things that apply to everyone regardless of experience level.
With this in mind, here are a few points to note:
1. Before starting the investigation have everyone in the group form a line side by side and take a group photo. They should be dressed as they will be for the investigation. Also in this picture have one of the group hold a sheet of paper with the time written on it large enough to appear in the picture. It sounds silly but it serves two important purposes. First, it shows what everyone present is wearing for that inevitable time someone accidentally wanders into your field of view about the time you snap a picture. Yeah, it happens even with a well organized investigation! But it makes it a lot easier to debunk that shadowy figure that appears to be wearing an orange shirt if you can match it up with your group photo. Also it establishes the precise time frame on all your photos. Digital cameras imprint the date and time as a part of the EXIF data on each picture. Hopefully you have set your camera's clock and it is correct, but even if it is off you can compare the time written down to the time the camera stamped the image to determine a correction factor.
2. Always take at least two pictures when you snap one. They should be as close to the same position as you can get and as quickly as possible to the same time. If using flash that would be as soon as your flash recovers and is ready for the second shot. Two to three seconds is often all you need. If something is present in both chances are it was really there. If its in one and not the other the probability is that you have either captured a spec of dust or insect flying by or maybe it is simply an anomaly created by the camera.
3. Related to Number 2, if you observe something and it appears to be persistent take multiple photos. And if your camera allows for manual adjustment it is often a good idea to intentionally overexpose and underexpose a few shots. (The two pictures rule applies; take two of each exposure setting.) Also if possible shift your position to get a different perspective on the subject. I realize situations where this many shots might be made are rare, but the more images you can get under different conditions the better it is when it comes time to analyze your evidence.
4. If you are investigating at night note the position of any light source in the area. If at all possible turn so that light is not in or near the field of view. Lights can induce lens flare or saturation which will create artifacts in your picture. This type of false positive, next to dust orbs, is probably the most common source of anomaly seen in images claiming to show paranormal activity.
5. Hold your breath while making a picture! Even better hold it for at least 5 - 10 seconds before snapping the shutter. Breath has a way of getting in front of the camera and when that happens your flash will illuminate it brightly. You will capture fog and mists in front of whatever you are photographing. And there is no shortage of wannabe believers who will attribute this to spirits, ectoplasm, or some other paranormal source. So the best thing is keep it out of your pictures whenever possible. And also note that no matter how hard you try, under humid conditions such mists will turn up. Perspiration and dampness in your clothing can also evaporate causing the same conditions, so while you may not be able to prevent it completely at least you can be aware of it and take measures to reduce the effect.
6. And if you manage to get something significant resist the urge to modify it in any way. Keep the original file intact as it contains information about the camera and image that will help study it. All digital cameras, even cell phone cameras, generate this data. If you intend to share it online be aware that some sites, notably Facebook among others, compress the image and render it useless as evidence. Any analysis will have to be done from the original file or a direct digital copy of it. You can read more about the metadata / EXIF data under Questions related to Cameras.
These are just a few basic things to help get you started into the field of paranormal investigation. As I stated this is the area easiest to get your feet wet, so to speak. You may already have a camera so it involves no costs. Later if you decide to get into it deeper you can buy better cameras or branch out into other areas such as EVP or EMF monitoring. But as a starting point, the best thing is connect with a reputable investigator and arrange a field trip. Enjoy Yourself!