This passage can be confusing when trying to understand what God looks like and how we experience Him. The people are instructed to not make any image of God, and Moses reiterates over and over that they did not see a specific form when God came down on the mountain. Many people use this, along with the phrase “God is spirit” in the New Testament (John 4:24), to say that God is formless. However, it seems clear that the reason God did not want them to make an image of Him is that the nations all around them worshipped images, and the danger was that Israel would do so as well. This does not necessarily mean that God does not have any form. In fact, Moses saw God “face to face” (Deut. 31) and also asked to see God’s presence, and God showed him His “back” (Exod. 34). Both of these passages imply that God does have a form; it is just that He is so beyond our comprehension that we cannot make an image because it would lessen God.
In addition, when Jesus shows up in the Old Testament, He often appears as an angel, and people are able to see Him. In Daniel 3, Nebuchadnezzar recognizes that the being in the furnace with the three Hebrews is divine but appears like the “son of man,” also implying that God is a personal being whom we look something like. Indeed, this could simply be the form that God chooses to take. But this may also hint at what it means to be made “after God’s likeness” in Genesis 1:28, in that we look the most like God of any of His creatures (“likeness” is the word used elsewhere for appearance, as in Gen 12:11; 24:16; 26:7, etc.). In contrast, being made in God’s image likely implies our functional role as rulers of the earth in God’s place.
All through the Old Testament, God is described as having a face, eyes, ears, hands, arms, legs, and so on. For example, when God appears on his fiery throne to Ezekiel, and again in Daniel and Revelation, He is described as we might describe a person (or, more accurately, we are described as similar in appearance to God). While this could simply be anthropomorphizing language and must be on some level because we are not God, the preponderance of evidence implies that there is something more here to be understood. Indeed, the things that the people were not to worship are listed: humans, all animals, sun, moon, stars. God is far beyond our comprehension and understanding, and yet He is also close to us, lives in our hearts, and ultimately humbled Himself to become a human.