ZikrAllah and Ibadah

Salam Sayyadi Dara, May Allah always keep you under the shadow of His love.
I was wondering about the meaning of Zikr-Allah, the remembrance of Allah. What does it mean in the Quranic sense and Sunnah sense? How do we do it? I have been told to repeat certain names of Allah or certain Ayahs from Quran. Is that the recommended way for Zikr?
I also sometimes wonder about the meaning of Ibadah. What does it mean in Quranic sense, and Sunnah sense? How do we do it? I have been told to do the ritual Salah in large number of Rakah. Is that the preferred way to do Ibadah?
Wassalaam