Which bible character prayed earnestly and effectively and got their prayers answered?

That was Elijah. In James 5:16-17 it says -

".........The effective, fervent prayer of a righteous man avails much. Elijah was a man with a nature like ours and he prayed earnestly that it would not rain, and it did not rain on the land for 3 years and six months".

and in v.18 it states -

"and he prayed again and the heaven gave rain and the earth produced its fruit."

This particular story of Elijah is found in 1 Kings, chapter 17.