Limits aren't that bad Indigo. A limit is a way to describe a function's activity (if you will) near a certain number (reiterating what's been saying and adding some stuff, never hurts to get the same idea in different ways). If you're just starting with limits, you may not be be dealing with limits at infinity that much.
A Limit is the value that a certain function approaches as x approaches some number. So consider the function y=(x^2-9)/(x-3) This function will look a lot like the function y=x+3 [(x^2-9)/(x-3) = ((x+3)(x-3))/(x-3) = (x+3)] However, it does not exist at x=3 [x-3=0, can't divide by 0]. However, we can describe what the function seems to be doing at three from what's happening around. [I apologize, but I don't feel like doing out a whole chart]. From the left, the graph seems to be going to 6 as x is going to 3, and the same from the right. The Graph will get impossibly close to 6 as x gets impossibly close to 3. Therefore, the LIMIT that they are approaching is 6.
A mental image you could use to imagine this is to imagine yourself moving along a graph [for this one, lets use y=(abs[x-3])/(x-3), abs[] means absolute value) from right to left (positive to negative). At x=3, that would be a cliff edge. If you stay at some point where x>3, you don't fall, and if you move to some point where x<3, you fall (in order for English to work properly, you don't want to fall). Because of this, your limit of motion is x=3. You can move up to this point, but you can not go past it, and if you stand on x=3, something weird happens. You have both fallen to and stayed at y=1. This is why it is said that y does not exist at x=3, but your limit of motion is three. (this specific example is would be the Limit as x approaches 3 from the right ["lim" with "x=3+" written under it]).
An important thing to watch out for is when the limit does not exist. This happens when there's oscillating behavior [like the limit of sin(x) as x approaches infinity], or the limit approaches two numbers from different directions [like y=(abs[x-3])/(x-3)]. Another thing to watch out for is when the function value is not the same as the limit. This is usually obvious (piecewise functions), but it can sometimes catch you. Make a habit of looking at the graph of a function when finding a limit (or have a mental picture of what the graph approximately looks like). If you have a line, and one point is not in that line, the limit is what the line approaches, not the stand alone point.
If I think of anything else, I'll edit it in here.
