The exact reasons for newborn babies suffering hiccups more so than other, older, infants is not generally agreed upon by the medical profession, but undoubtedly much has to do with the relative immaturity of your baby's internal organs. As your baby develops and matures, so too will the hiccupping reduce in intensity and frequency.
There isn't a lot you can do to stop the hiccups in a newborn baby. Certainly the old wives-tale solutions for adults (such as standing on your head, breathing into a paper bag, getting a scare etc.,) should not be tried on your infant. In fact, probably the only thing you can do is to patiently wait the hiccups out and try to comfort or distract your baby while the hiccups persist. Frequent burping during feeding may decrease the instances of hiccups, but once they start there is very little that you can do.
Hiccups can last for anything from a minute or so right up to half an hour or an hour at a time but they do not harm your baby in any way. You may find however that as your baby gets older, he/she will tend to get frustrated during periods of hiccupping. By this stage however your baby should be easier to distract and keep occupied and hopefully this in turn will make it possible for you to help your baby stop hiccupping once he/she starts.
Remember, at the end of the day it is only really the parents who get bothered by baby's hiccups. They don't bother your baby at all (in fact he/she probably wonders why everyone doesn't hiccup!), so the only things you need to give your baby each time hiccups develop are a little bit of patience, and a lot of TLC.