Notes about the schematics here: Stone brick indicates "any block", while gold blocks indicate opaque blocks (relevant to redstone). For a cobblestone generator, "any block" probably implies "fireproof". Water and lava source blocks may be marked with "s" when there is possible confusion. Cobblestone or smooth stone appear only where they form. An "x" indicates a place to stand while mining the cobblestone.
For the basic trench generators, you should place the water first, because if the lava flows before the water reaches it, it may "resist" the water and not form cobblestone. Of course, if you place them both fast enough, the lava won't have time to flow anyway. Design B is a variant of the basic "generator core", the center of most of the piston designs.
Design A is most basic of all (from this video) and safer, although it can lose some cobblestone to the lava unless a slab is placed over the lava. Design B (from this video) washes the mined cobblestone toward the player, so as to minimize loss. When building design B, you can leave a block where the cobblestone will form, and mine it to start the process.