"Back to Square-1"
I have a few of these shape-shifting beauties: here we see two original (?) Square-1 and a cheap DX.
There are quite a few methods to choose from depending on how much one wants to dedicate to efficiency and speed, the trade-off being the number of algorithms one is required to learn.
As I am still a beginner with this puzzle, I'll hand over to the wonders of YouTube and this excellent tutorial from Emile Compion. Many thanks Emile...
The steps described in Elmile's video are as follows...
Step 1: Get the puzzle into a cube shape.
Every Square-1 technique I've encountered so far has this same first step. There are many scrambled shapes but the edges and corners can be grouped intuitively with patterns that become easier to recognise with experience. See http://www.geocities.com/jaapsch/puzz... for details.
Step 2: Solve corners of top layer.
Emile describes this in the annotations and it is another intuitive step. Get a pair of top layer corners correct and hold them to the left. Bring another top layer corner, but NOT the right one, up into the Upper-Right-Back corner position. Position the final corner on the bottom llayer such that when the right side comes down it will match up with the corner from the top before bringing them both abck up to the top layer.
Try this a few times until you get the hang of it.
Now all the top layer corners are in the correct relative positions then the bottom corners will of course all be in the bottom layer if not in their correct positions.
Step 3: Edges to correct layers.
The following algorithm swaps the edges on the right between the top and the bottom layers. Perform multiple times if necessary.
Step 4: Bottom layer corners.
With a pair of corners to swap held at the front of the bottom layer...
Step 5: Permute edges in both layers.
With edges to permute on both layers on the right and back...
Parity: if required, with...
/(3,3)/(1,0)/(-2,-2)/(2,0)/(2,2)/(-1,0)/ (-3,-3)/(-2,0)/(3,3)/(3,0)/(-1,-1)/(-3,0 )/(1,1)/(-4,-3)
Fix the equator: if required, with...
Another method at http://nerdparadise.com/puzzles/square1/ with less algorithms to learn uses two "building-block" algorithms named "A" and "B" combine to make up a variety of corner and edge swaps.
A = (1,0)/(-1,-1)/(0,1)
B = /(3,0)/(-3,-3)/(0,3)/
I actually get the corners into the right layers intuitively - I suppose you could call this stage "corners OLL" although there's two last layers involved here, but it is distinct to the permutation of the corners which can be though of as a "corners PLL".
Getting the edges into the right layers requires an understanding of the A algorithm: this swaps two of the edges from the top layer with the opposite pair of edges on the bottom layer. By playing with this algorithm all sorts of edge swaps can be made: do the algorithm twice and all changes are reverted back to normal. Make upper and/or lower face adjustments between two A algorithms and various edge swaps can be made.
(todo - cover all cases)