Most normal pet birds never need to have their beaks trimmed. Many people will mistake the superficial flaking of outer layers for overgrowth. If the beak is actually overgrowing, it could be the result of an injury or deformity, scaly face mites (Cnemodecoptes), or liver disease. One common cause of liver disease in parakeets is obesity, which can result from a combination of genetics, excessive eating of high fat seeds, and lack of exercise.
I would highly recommend that you take the bird to an avian veterinarian for a checkup to see if a cause of the beak overgrowth can be determined. It may be something simple and treatable like the mites, so that once addressed, the beak will not be a problem anymore. As a side note, the mite protectors and sprays you can purchase at the pet store do not work on this type of mite, and are unnecessary in my opinion.
If it is more complex problem, like fatty liver disease from obesity, the vet can talk to you about making gradual changes in the diet, such as offering pellets and dark green leafy vegetables in addition to the seed. The doctor can then safely trim the beak, and may be willing to show you how to do it yourself. Beak trimming requires great care, because if you get it too short, it will not only bleed profusely, but the pain may prevent the bird from eating for several days. Every species has a different normal length, and even if you try to cut the beak to look exactly like a normal parakeet's beak, you may get it too short. Sometimes when the beak grows out, the blood supply will also grow out further than expected.
Here are some sketches and photos of overgrown beaks so you can compare your bird's beak to determine if it is really abnormal:
If you do attempt to trim the beak yourself, the most important thing to know is you must avoid holding the bird too tightly, because if you compress his chest he may not be able to breathe. The next important point is that you should usually trim less than you think you should. He can do okay with a beak that is a little too long, but as I said before, too short can be extremely painful and even life threatening.
Please feel free to write back if you have further questions about this.