For new people to skyblock, I suggest you look at a different thread for some more tips. I'll try to mention some of the easier stuff, but it's rather hard when I've been playing so long the easy stuff seems like common sense.

Starting the island: The first thing I do with my island is break that tree and put the results in the chest. Next I mine down into the dirt and make a cobble gen I can stand in and mine downwards. Also, I set up the water (ice you break for water) in a 2 by 2 area diagonal from each other so it makes an infinite water source. The way to make a cobble gen you can mine down is just a normal cobble gen with slabs above all of the water and lava blocks except for the block the cobble spawns on. If you do this correctly you can mine straight downwards and not be pushed away when the blocks respawn.

Once you have lots of cobblestone (5-6 stacks would be way more than enough) you can scoop your water and place it so it flows over the edge.
With only the cobble in your inventory you can carefully flow down the water fall and place blocks on the bottom of the island and continuing to do so down to y1. If you fall at any point quickly type /is
I would get the blocks down to y2 or y1 then make a platform

The third thing I do is make a reliable spawn point. You want this spawn point to be at the highest point you will build on your island, because it is easier to go downwards rather than up. This is a spawn point I always use because when you spam /is when you fall, you won't die. To make this spawnpoint you need 1. Water 2. A slab 3. 8 signs atleast and the command to reset your island spawn point. To start your spawnpoint, check the block you want to spawn on, and place your slab there. Next you will place your signs two high in a plus surrounding the slab. After placing the signs you place the water above the slab (won't flow out of you placed the signs correctly) and type the command to reset your island spawn. If you don't know te command do /is cp and hover over the icons to figure out which one resets your island spawn and click it. Now when you type /is because you fell off your island, you won't even die.

After making the bottom platform and spawnpoint, I go back to the original island. You'll need to use that water fall again and make a platform beneath the island equal with the bedrock, now you can collect all the dirt and sand without losing any. You will definately need this dirt, as dirt is one of the most valuable resources in skyblock.

When I collect the original island and cobble gen and chests etc, I move it all to the bottom level and begin the cobble gen again. I usually choose a block type or types to then that level, and make the first full island level. Building as far you can in any direction it will let you until you can't do it anymore.

Finally for this thread, I set up the farms using the dirt from the original islands, and proceed to complete all the challenges in /c that I can