The central metaphor of the first half compares the Lord to a shepherd and the speaker to a member of his flock. He's like, "I'm just a sheep," which we'd say is pretty humble. We associate sheep with followers.
He maketh me to lie down in green pastures: he leadeth me beside the still waters. (line 2)
The speaker admits he has been rather blessed. But he humbly gives all the credit for his happy conditions to the Lord. He hasn't really accomplished any of it on his own. He means that he could not have accomplished anything without God's assistance.
He restoreth my soul: he leadeth me in the paths of righteousness for his name's sake. (line 3)
Here again we get that strange mix of pride and humility. He's like, "I'm a good person!" But he adds, " ...Only because the Lord wanted to express the goodness of His nature." The speaker's goodness is a way of glorifying God's "name."
thy rod and thy staff they comfort me. (line 4)
A rod and a staff are basically the same thing; they're used to guide sheep when they stray off the path and away from the flock. The poet Gerard Manley Hopkins picked up on this image in his poem "God's Grandeur," where he writes, "Why do men then now not reck his rod?"
Surely goodness and mercy shall follow me all the days of my life: (line 6)
This means: "As long as I continue to trust in the Lord, things will continue to work out in my favor."