Dana and Mantey's Manual Grammar of the Greek New Testament provides a visual to explain the direction implied by prepositions. You may want to try to draw it yourself. In the center is a circle, from which radiate arrows away from the circle on/to the right, top and bottom. When coming from the left arrows go to, into, and through the circle. Inside the circle is one preposition and one preposition describes the circumference.
The preposition that designates the circumference in English is 'around' and in Greek it is peri, as in the word 'perimeter'.
"The distance around any circle (or its perimeter) can be measured using the formula 2πr."
The preposition that is entirely inside the circle in English is 'in' and in Greek, its cognate en.
"The man elected president works in the Whitehouse."
The first word of the Gospel of John is en from "in the beginning."
Leaving the circle, but starting from the inside is a compound in English ('out of'), which is a single word preposition in Greek ek. (Draw an arrow from the interior of the circle to the right perimeter and beyond.)
"The person named 'it' had to stand out of the circle."
In the Gospel of John 1.13, children are described as born ek theou 'out of god'.
From the perimeter of the circle to the outside is the English preposition 'from' and its Greek equivalent apo (Another right-bound arrow).
"From the circle to the outside."
A preposition on the outside of the circle that doesn't show movement but still shows a spatial relationship is the English 'beside' rendered in Greek as para. (This can be placed on a line perpendicular to the arrow for from/apo.)
"His irrelevant objection was beside the point."
See John 1.6 for a Greek use of para.
A preposition that begins on the left side of the circle and moves to its edge is 'toward' in English and pros in Greek. (Draw an arrow from the left to the perimeter.)
"The basketball player walked toward the foul line."
In the Gospel of John 1.1, the preposition pros is used with ton theon.
If the movement doesn't stop at the edge, it goes 'into' or ]eis. (Draw an arrow from the left and on through the perimeter.)
"He walked toward the door and then into the room."
If the movement doesn't stop at the interior but moves all the way across, the English preposition is 'through,' which in Greek is dia. (Draw an arrow from the left through the perimeter on the right.)
"He walked through the room to the door on the far side."
In the Gospel of John 1.3, where everything came into being "though him," the preposition used is dia.
A preposition that shows that something is just touching and over another object is one that is 'upon' it, or epi in Greek. (Draw a horizontal line tangent to the top of the circle.)
"'Swift-footed' is an epithet of Achilles because it is a name that is put upon him."
Prepositions can also show that something is over or under. If something is over, but just, it is 'upon' the object, which in Greek is epi. If it is further away, it is 'over' or hyper or it is 'under' or hypo. These Greek prepositions are familiar in words like "hyperchondriac" and "hypothermia". (Draw horizontal lines over and under the circle running parallel to the line for 'upon'.)
The English prepositions 'up' and 'down' are ana and kata in Greek. (Draw arrows up and down from the perimeter of the circle.)
"He walked down the stairs and up the block."