If you want to wish someone a good start of Ramadan, it is customary to say "Ramadan Mubarak", which means "Blessed Ramadan". You can also say "Ramadan Kareem", which translates as "Generous Ramadan".
If someone says Eid Mubarak to you, it is polite to respond ... the breaking of the fast ‘– it is celebrated at the end of ...
Most Muslims use the Arabic phrase "Ramadan Mubarak," which translates to "have a blessed Ramadan" or "happy Ramadan, to greet each other. The English translation "Happy Ramadan" works just fine.