In John's Gospel, Jesus said, "I am the living bread...Whoever eats of this bread will live forever...Unless you eat the flesh of the Son of Man and drink his blood, you have no life in you...."
From Psalm 34: "Taste and see how good the Lord is...Those who turn to the Lord shall not lack any good...I will teach you..."
In John, we read "I live because of the Father, so whoever eats me will live because of me."
I think it's a mistake to interpret this promise as being restricted to some life after we die. Rather, I think Jesus is promising us a new life, right now. And Psalm 34 helps me see what that life can be like for someone who has tasted and has seen how good the Lord is--a life in which we keep our tongues from evil and our lips from deceit; a life of departing from evil and doing good and seeking peace.