Epsilon-delta definition of limit? Please help this 8th grader!

So, in my textbook, we just finished "differentiation" and some parts of "application of Derivatives" and "detailed graphing"

I understand the concept of limits, but this epsilon delta definition is confusing me.

Can you explain to me how to do this?
Please explain what each of these symbols actually mean, and how to figure out the epsilon (or error), delta, and how can I prove the function.

Okay - the point is that no matter how small an epsilon you pick to describe how far away from the function value you are (VERTICALLY), you can pick a value of delta > 0 to describe how far away you are HORIZONTALLY to be within that bound.

For example, if f(x) = x/10,000, the limit as x -> 10,000 = 1. If you choose epsilon = .000001, then you need to find delta such that |f(10,000+delta) - f(10,000)| < .000001

f(10,000 + delta) = 1 + delta/10,000
f(10,000 + delta) - f(10,000) = delta/10000 < .000001
delta < 0.1

So if delta < 0.1, the function will be within 0.000001 of f(10,000).

The point of the proof is that you can choose an arbitrarily small epsilon, and still have delta > 0.