"The Lord God made garments of skin for Adam and his wife and clothed them." NIV translation
God demonstrates His love for them (and us) in that He made clothes for them. He did this because He loved them so much that He did not want them to be ashamed of their bodies. To make the clothes out of skins, blood had to be shed as the animals had to die. This was a picture of the sacrifices that were to come under the Jewish Law as well as a picture of the perfect sacrifice which is Jesus Christ. We notice that God made the clothes for them instead of telling them to do so for themselves. This is a reminder that salvation does not come from our work but is a gift from God.
"And the Lord God said, 'The man has now become like one of us, knowing good and evil. He must not be allowed to reach out his hand and take also from the tree of life and eat, and live forever.'" NIV translation
After the sin, God had to act to prevent man from living forever in the fallen state. He says, here, that He could not allow the fallen man to also eat from the tree of life but the reason for this is not another punishment. The reason that Adam and Eve could not be allowed to eat from the tree of life is that they would be trapped in the effects of their sin forever.
"So the Lord God banished him from the Garden of Eden to work the ground from which he had been taken. After he drove the man out, he placed on the east side of the Garden of Eden cherubim and a flaming sword flashing back and forth to guard the way to the tree of life." NIV translation
Many see this as a continuation of the punishment of God for their sin but it is not. In the previous passages, God issued the punishments but now they are sent from the garden out of love. The simple fact is that most people want to live forever and would have tried to get to the tree of life to make that happen. God, because of His love for us, sent them away from there and put a guard on duty to keep this from happening. This was necessary to keep man from living forever with the effects of sin.