A sump can be as simple as a smaller aquarium inside the stand of the big one. Water drains into it via gravity from the main tank, and a pump sends it back up.
The complicated part is how you drain water from your big tank. Your tank will either have holes already drilled in it for this purpose or not.
If your tank already has holes, it probably already has what's called an "overflow box" around the hole (this is commonly called a "reef-ready" tank). The primary purpose of this box is to define the water level in the tank: if the hole is at the bottom of the tank and there is no overflow box, all the water in the tank can drain out!
If you have no holes, one common solution is an item called a siphon (or "hang on back") overflow. This is basically two plastic boxes, one that sits in the tank and one just outside. A U-shaped plastic tube connects them and water flows from the inside box to the outside box; and from the outside box down a pipe or a hose to your sump. The boxes are set up in a way that the siphon won't break if it water flow stops. Given that, some siphon overflows should be avoided like the Plague (particularly Marineland and CPR brands). The best brands are Lifereef, Amiracle and Hurricane.
Another option if you don't have holes is to make holes. With a special diamond-coated hole-saw ($10), a power drill and a little patience, an amateur can drill holes safely and quickly in an aquarium. I personally think this is an infinitely better solution than using a siphon overflow. If you drill your own holes you will also need to install some sort of overflow box, for the reason described above; however this isn't too difficult.
The important trick is to find a way to make the overflows escape proof, since octos can find their way into very small places. A bit of fiberglass window screen and a lot of creativity go a long way!