Part 1: Solving the 1st Layer

Section 1-1: Make a plus sign on the 1st layer

Pick the color you want to solve first. Hold the cube so that the center piece of your chosen color is facing upward.
In section 1, we will make a plus sign of the color you chose using the edge pieces that contain that color. We will only worry about these 4 edge pieces, not the corners.
Move on to step 1-1b.

Find an edge piece that has the color you picked and take note of the other color on that edge piece. Move that piece so that it's in the edge position that touches the center pieces that match these 2 colors.

If you're repeating this step: be careful not to move any already solved edge pieces out of position while doing this. It can be helpful to move the edge piece you're currently working on to the bottom layer (opposite your chosen color's center) to keep it out of the way of previously solved pieces, then rotate it 180 degrees to move it next to your chosen color's center without ruining your previous work.

NOTE: A common issue during this step is that you may have an edge piece placed in the top face next to the center of your chosen color, but the edge’s sticker of the same color is flipped so that it is not next to your chosen color’s center.

If this is the case, hold the cube so that your chosen color's center is facing up and the edge piece that's flipped in the front layer, pointing towards you, and perform algorithm 1

Repeat this step until all 4 edge pieces of your chosen color have been solved. These pieces are solved if there's a plus sign of your chosen color and the color of the 4 edge pieces forming the plus sign match both the colors of the center pieces they're directly adjacent with. Then move on to section 1-2.

Before you start this section, you should have a plus sign of your chosen color solved. Each of the edge pieces of the plus sign should be aligned with both of the center pieces that correspond with the 2 colors on that edge piece. If not, go to section 1-1.
Algorithm 2 (don’t perform it until specified) swaps the two corner pieces that are shared by the front and right faces and rotates each of these corner pieces each time it is performed. This is the only algorithm needed for this section .
Move on to step 1-2a.

To solve the corners of the 1st layer, hold the cube so the plus sign you made is on top fig. 5. Find a corner spot with an unsolved (solved = all 3 colors on the corner match the centers of their corresponding faces) corner in the top row and hold the cube so that this corner is in the top, right, front position fig. 6, but make sure the plus sign you made previously stays on top (note this corner positioning. We'll be using this for several algorithms throughout this tutorial)

This corner should either be in the correct position but the wrong rotation (go to step 1-2b)

If the corner you’re looking at is in the correct position but the wrong rotation, perform algorithm 2 repeatedly until the corner is solved (i.e. in the correct position and rotation).
Repeat this entire section (1-2) until all 4 corners are in the correct position and rotation, and the face of your chosen color is completely solved. Move on to part 2 ▶.

If the corner you’re looking at is not the correct piece for that spot at all, then locate the piece that does belong in that location while making sure to keep holding the cube so that your plus sign is on top.

If the corner you just located is in the top layer of the cube (the one you decided to solve first), then hold the cube so that the corner you just located is in the top, right, front position fig. 6 and perform algorithm 2 once. The piece should have moved to the bottom layer, and you can now move on to the next bullet point.
If the corner you just located is in the bottom layer of the cube, then turn the bottom face so that the corner is directly beneath the spot in which it belongs. Hold the cube so that your plus sign is on top fig. 5 and the corner you’ve located is in the bottom, front, right position. Perform this algorithm 2 repeatedly until the corner is solved.

Repeat section 1-2 until all the corners of the 1st layer are solved, then move on to part 2 ▶.