So, firstly when you have to reach Greater Noida from New Delhi Railway Station. In Delhi now we have got Metro which is very good, cheap, fast and traffic free transport system. If you are at New Delhi railway station or any where in Delhi and you want to reach Greater Noida, just go to the nearby Metro Station and buy a coin(ticket) for Botanical Garden Metro Station ( Botanical Garden is a place in Noida. Whether you are from New Delhi or Gaziabaad or any other nearby NCR you will first have to reach Botanical Garden first for going to Greater Noida.).
After buying your coin aboard the metro. Please note there is no direct metro from New Delhi Railway Station to Botanical Garden, so you will have to aboard the train for Rajiv Chowk, after you reach Rajiv Chowk you will have to change metro for Botanical Garden (Noida).
After you reach Botanical Garden Metro Station, come out of the station and you will find various Yellow buses or low floor buses that will take you to Parichowk (Greater Noida), from where you can further go to your final destination via sharing or hiring auto.
There are private buses also but we advice you or we just highly recommend you Government Bus Services, because private bus drivers of Greater Noida are very careless, not responsible at all, they will take double time than usual Government Buses.
Now if you want to reach Greater Noida from Gaziabad you can catch a Yellow Government Bus to Botanical garden from where you can further aboard another bus from Botanical Garden to Parichowk.
Note :: If you are lost somewhere in New Delhi or anywhere and you want to reach Greater Noida, just reach your nearby Metro Station and follow the above told route.
NOTE :: We highly recommend you to use Government Buses only, because they will take less time, are cheaper and safe. Although cost doesn't matter so much but your safety does. This is from my personal experience.