The purpose of prayer is expressed excellently by the verse of Psalm 34:5:
“Draw near to Him and be enlightened.”
The purpose of prayer is, simply put, the experience of prayer. And this is coupled with contrition and tears. Tears of repentance are born only through prayer. And prayer again is born only through tears of repentance. St John Climacus stressed this by saying that prayer is “the mother and the daughter of tears.”
Genuine prayer needs the following:
The atmosphere of prayer must be one of mourning, contrition and repentance. A “broken and contrite heart God will not despise.” (Psalm 51:17)
Each of us needs a quiet place to pray. There we should have our icon(s), oil lamp, incense, prayer books, and definitely privacy and quiet.
We can pray for others, in general terms and for specific people, mentioning their names, for living people and for people who have died. Hopefully we do not hate anyone, but, if we do, we need to pray for them.