Paraphrasing the Summa: First part, Question 2, Article 2

Question 2. The existence of God

Does God exist?  

Article 2. Whether it can be demonstrated that God exists?

Can we prove to people that God exists?

Objection 1. It seems that the existence of God cannot be demonstrated. For it is an article of faith that God exists. But what is of faith cannot be demonstrated, because a demonstration produces scientific knowledge; whereas faith is of the unseen (Hebrews 11:1). Therefore it cannot be demonstrated that God exists.

The first objection says that if you prove God's existence, then you do away with faith.  Because if you can see something, you know it is true and you no longer hope that it is true.

Objection 2. Further, the essence is the middle term of demonstration. But we can not know in what God'sessence consists, but solely in what it does not consist; as Damascene says (De Fide Orth. i, 4). Therefore we cannot demonstrate that God exists.

We can't prove a negative.  God's essence is far beyond a human capacity to understand.  Therefore, God's existence can't be proved.

Objection 3. Further, if the existence of God were demonstrated, this could only be from His effects. But His effects are not proportionate to Him, since He is infinite and His effects are finite; and between the finite and infinite there is no proportion. Therefore, since a cause cannot be demonstrated by an effect not proportionate to it, it seems that the existence of God cannot be demonstrated.

It is not true that God can be known by studying nature.  Because is infinite and nature is finite.  Therefore, there is no relation between God and nature.  And God's existence can't be proved by nature.

On the contrary, The Apostle says: "The invisible things of Him are clearly seen, being understood by the things that are made" (Romans 1:20). But this would not be unless the existence of God could be demonstrated through the things that are made; for the first thing we must know of anything is whether it exists.

But, St. Paul says, in the book of Romans, that God's existence can be proved by His creation.  Therefore, since we know that we exist and we are wonderfully made, then we know that our Creator exists.

I answer that, Demonstration can be made in two ways: One is through the cause, and is called "a priori," and this is to argue from what is prior absolutely. The other is through the effect, and is called a demonstration "a posteriori"; this is to argue from what is prior relatively only to us. When an effect is better known to us than its cause, from the effect we proceed to the knowledge of the cause. And from every effect the existence of its proper cause can be demonstrated, so long as its effects are better known to us; because since every effect depends upon its cause, if the effect exists, the cause must pre-exist. Hence the existence of God, in so far as it is not self-evident to us, can be demonstrated from those of His effects which are known to us.

St. Thomas argues that there are two ways that God's existence can be demonstrated.  One way is to argue from the point of view of the Creator.  The other is to deduce His existence from what He has created.  Since we know that some things are created which are too wonderful to exist unless they were created, then we can demonstrate the existence of the Creator.

Reply to Objection 1. The existence of God and other like truths about God, which can be known by natural reason, are not articles of faith, but are preambles to the articles; for faith presupposes natural knowledge, even as grace presupposes nature, and perfection supposes something that can be perfected. Nevertheless, there is nothing to prevent a man, who cannot grasp a proof, accepting, as a matter of faith, something which in itself is capable of being scientifically known and demonstrated.

I can only speak for myself here.  The way I understand St. Thomas is to say that FAITH IS BELIEVING.  And believing is knowing.  When you believe something, you know it is true.  That is why, to an atheist, seeing is believing.  Because once he sees it, he knows it.  But to a Catholic, faith is believing.  Because, once we come to accept the truth of God's existence, we begin to know Him and to love Him.

Folks, the most pitiful thing I have ever seen is a Catholic or a Christian, having just been asked the question, "Do you believe that God exists?"  Answering, "I don't know.  I have faith that He exists."

That is not faith!  THAT IS IDIOCY!  Faith is trust.  Faith is love.  Faith is knowing that God is a rewarder of those who diligently seek Him.

Reply to Objection 2. When the existence of a cause is demonstrated from an effect, this effect takes the place of the definition of the cause in proof of the cause's existence.

The existence of a creature, demands the existence of a Creator.

This is especially the case in regard to God, because, in order to prove the existence of anything, it is necessary to accept as a middle term the meaning of the word, and not its essence,

???  I have no idea what he means by middle term.

for the question of its essence follows on the question of its existence.

We don't need to know God's nature in order to prove that He is real.

Now the names given to God are derived from His effects; consequently, in demonstrating the existence of God from His effects, we may take for the middle term the meaning of the word "God".

 I still don't know what he means by "middle term".

However, from the context, I assume he is simply repeating that God can be proved by His effects.

Reply to Objection 3. From effects not proportionate to the cause no perfect knowledge of that cause can be obtained. Yet from every effect the existence of the cause can be clearly demonstrated, and so we can demonstrate the existence of God from His effects; though from them we cannot perfectly know God as He is in His essence.

Although nature is finite and God is infinite, yet we can prove God's existence from what He has created.  And, although our knowledge of His essence can not be known perfectly, we can get some knowledge of His essence from what He is not.