Since I don't know how much mathematics you know, let me try without (although this makes things more obscure than they are)
Quantum entanglement and the usual double slit experiment are unrelated.
First let's have a look at entanglement, since that seems to be what you really want to have a look at.
Imagine two parties, let's call them Alice and Bob, that share some object, for example a piece of (completely) magnetized iron. Now Alice measures the direction of the magnetization on her side of the piece and Bob does the same on his side. We assume that the direction of the magnetization is the same everywhere, since it's completely magnetized iron. That implies that Bob and Alice will always measure the same magnetization, their results will be perfectly correlated (e.g. Bob measures "up", then Alice has to measure "up", too, if they have agreed on what "up" means). You can produce similar scenarios with different kinds of correlations (maybe, they both draw a ball from a box containing 50% blue balls and 50% red balls in an infinite amount, and they measure the colour of the ball - in that case, the result will be uncorrelated. If Bob measures "red", he has no clue as to what Alice will measure).
However, there are correlations that are not possible in our classical world. This happens if you consider other types of measurements. And that is where quantum mechanics comes into the game. "Entanglement" is just another name for "correlations between experiments by Alice and Bob made on a shared system that are not possible in classical mechanics".
What I have described above, the experiments with "Alice" and "Bob", is what is called a bipartite system, where you might have bipartite entanglement. Likewise, you could have a look at a system with three parties (tripartite system) or as many parties as you like (multipartite system). In principle, this means that you can have entanglement between as many pieces of matter as you like - with some boundaries on the type of entanglement (e.g. "monogamy of entanglement", but for your current understanding, you don't have to consider the boundaries, because they require more background). It is true, however, that multipartite entanglement is as to now poorly understood mathematically. That means, we can describe it no problem, but e.g. comparing two multipartite system is a mess.
Now let's have a look at the classical double slit experiment, where you send one photon through either of two slits (randomly). It then appears (as long as you don't look where the particle went through), as if the particle went through both slits at once. Since there is only one photon involved, we cannot speak about "correlations", hence there is no entanglement. The question, why it looks as if one photon had "split" and gone through both slits simultaneously is a different one.
Last but not least, since it has been mentioned, a comment on the double slit quantum eraser. Here, we make the experiment with one part of a pair of entangled photons. The experiment (I won't describe it here, since the link was given), again, is very counterintuitive, because it seems as if we could influence the past. However, there is nothing mysterious, once you accept the conclusions drawn from the usual double-slit experiment and entanglement. There is no shift of paradigm, nothing has turned up in that experiment that we cannot yet explain in quantum mechanics.