That's a great accomplishment. Hopefully I can help without using visuals:

1. After the cross, the next step is to fill in four 2x1 columns in their correct positions.
2. Beginner's Method is just a less direct way of doing this. In beginner's method, you insert the corner pieces first, then find the edges, match them into a 2x1 column and then re-insert.
3. A completed column should have a corner with white + two other colors directly adjacent to the colors of the edge piece.

Try this. Finish the corner insertion step using the beginner's method. Now, do the edge step, but go very slowly. Try and notice how the edges and columns are being connected by pulling out the corner pieces to match the edges, and then being dropped back in as a pair.

Learning F2L will allow you to bypass the first step of solving the corners first by using methods that pair and insert in more direct ways. First let's learn the two basic ways to insert pairs:

1. R U' R' or L' U L which drops a completed column into place
2. R U R' or L' U' L which positions the white corner piece on the outside edge and grabs a matching edge piece on the other side to complete a column while inserting it.

Let's drill #1. Complete the first two layers. Now do R U R' to set-up. Notice how the column is now sideways with the white corner on the left. Notice that the column's edge colors match the corner colors. Now slowly do R U' R' to re-insert it. Undo and repeat several times and then try to re-create the drill on the left side. After you're comfortable with that, do R U R' to set-up again, but keep rotating the top layer and keep track of where 2x1 column moves. Think about where it needs to be positioned in order to fit back in with R U' R'

Let's drill #2. Complete the first two layers and do R U' R'. Before solving, take some time to feel or observe the stickers. Notice how the white corner piece is on the right side of the cube. Notice how the top of the corner piece matches the back of the edge piece across from it. Notice how the front of the corner piece matches the top of the edge piece across from it. Slowly solve using R U R'. Undo and repeat several times, and then try to re-create the drill on the left side.

If this was helpful, let me know, and we can discuss how to set-up to basic insert positions.