Many people have the vet or the groomer do this but you can also trim nails yourself. I find that mine keep their nails at the right length from regular walks on pavement but some dogs have nails that grow faster, or the dog may not wear them down naturally for a variety of reasons.
You can use a special file and file them down if you want to be extra cautious. Some people find nail grinders easier to use, and there are a few styles of nail clippers, such as guillotine type nail cutters. If you are buying a nail cutter get one of good quality so that the blade is sharp and the cutter is the proper size.
Many people don't realise that dog nails are fairly long anyway, probably longer than you think is the right trimmed length. So don't just dive in and start cutting! Be sure to have a good look at the pictures and directions below first. Remember that dewclaws also need trimming -- they can grow in a complete circle. Too-long nails can become very uncomfortable and even painful for a dog to walk on and I've seen neglect cases where the nail has grown in a circle and back into the dog's paw -- at which point you need a vet to repair the damage.
This page has very clear directions and recommends a Resco guillotine cutter for nails. Be sure to read the whole page before you start! Better yet, have your vet or groomer demonstrate for you once or twice so you know what to do.
This page is also a must-read as it has further detail and trimming tips: