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The 3x3 First 2 Layers

Now, we aim for solving the rest of the first 2 layers. The rest? Well, after you've solved the first layer (and assuming you did the cross right...) all that's left are the 4 middle edge pieces that make up the F2L.

What we do is we look for them on the top face.

An example of an edge piece we want.

As you can see, I have a red-green edge piece and it wants to go to where the red-blue edge piece is.

So put it into place, you align the face that's on its side with its relative center.
(As you can see, I've already matched my red-green edge piece with its green center.)

If the piece wants to go left, do this: U', L', U', L, U, F, U, F'.
If the piece wants to go right, then do this: U, R, U, R', U', F', U', F.

If you did it right, it should slide in with the corner piece.
Do this for all the edges, and you're done.

Non-edge Cases

Sometimes, you might not be able to find any edge piece at all. You might get something like this...

Sometimes, you might get no edges at all to work with.

When you get something like this, what you can do, is scramble a corner.
Of course, don't scramble a corner with an edge piece already solved there.

Also, you might get something like this:

Some irregular edge...

Where all the other 3 edges are solved and you're just stuck with this irregular one...
To solve it, just do the same thing: scramble that corner and try again.

Of course, you should always practice, and practice until F2L (and I mean ALL of F2L) and fluent for you.
Next up, OLL...

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Beginner's First Layer. Orienting the OLL!
      Back to the First Layer...                Getting closer...