We recommend that you take the Airport Hopper service from Dublin airport. They run a regular service from Dublin Airport to Maynooth Town. The student fare is currently c.€7. You can get off the bus at the last stop which is opposite the Glenroyal Hotel.
Maynooth University South campus is a 15 minute walk from this stop; the North Campus is a 20-minute walk from this stop. Please see map here:
If you have a lot of luggage, student assistants can help arrange for a local taxi company to collect you and bring you to campus (approximate cost €6).
Alternatively you can take a taxi from Dublin airport to Maynooth. You can pick up a taxi at the taxi rank at Dublin Airport. The approximate cost is €70 one way.