You don't have to posses any special equipment or expensive devices. There is obviously such stuff, but it's mainly used by professional private investigators as well as law enforcement. In some cases big telemarketing companies also employ it, but for an ordinary person who just want to hide his or her phone number from the eyes of the other person, there is a cheap and simple solution. It works like a calling card - at first you dial the number given on the card and then upon a few moments you will be able to call the number you need. The cost of such operation will be slightly higher than when calling without spoofing ID, but thanks to use of such a calling card, you can be sure that the person will not know your phone number.
Many people will think that they can use a feature built-in their cell phones in order to hide their phone number when calling. Unfortunately, this is not as effective as the calling card fro spoofing ID and can be easily tracked without any bigger effort. Which means that there is no point in making use of it if you have to stay anonymous. There are a lot of different companies who offer calling cards for spoofing IDs and you should always compare prices, since almost all the services offer the same features, so it's smart to choose the cheapest one.
There is a very important thing which you should bear in mind when spoofing ID. It will never make you 100% and when you break the law, it will not be difficult to trace you and find out your real identity. Of course, this can't be done by an ordinary person, but only by law enforcement agency with a court injunction. This means that you can safely use a spoofing ID for each and every legitimate purpose without thinking of any legal consequences.