The easiest/quickest way to divide a tank is to hit Walmart or a craft store and buy some craft plastic canvas and report (as in school report) binders. Cut the plastic canvas to fit the tank, silicone the report binders to the sides (although I do have some tanks where they're not permanently attatched...I don't recommend doing that until you're positive they won't shift and let the fish through), and then stick the canvas into the report binder clips. You can use a regular old hang-on-back filter, corner filter, or sponge filter for this type of divided tank, anything will work since the water can flow freely through the canvas.
A more lengthy way of dividing a tank is to purchase some plexiglass (note, plexiglass is a brand name, if you buy the generic stuff you'll save a TON of money), follow the directions below. I designed this for use with a hang-on-back filter, but you could put a seperate corner filter in each compartment (then you could get rid of the back panel, that's basically to guide your current from the hob filter throughout the tank).
The way I have the plexiglass set up, the notches on the front-to-back dividers fit into the one side-to-side divider, so if you cut it very accurately, you don't need to seal the edges of the dividers to the tank glass (I hate permanent setups since i'm always changing my tanks around). Just make sure you're really, really accurate when you're cutting so you don't have any gaps between the divider and the tank walls, bettas can slip through surprisingly small spaces. Because I don't adhere it to anything, it should work in any tank (the plexiglass...the canvas i'd recommend silicon to hold to the sides of the tank since it's sort of flimsy).
One final note on the plexi construction - it really helps to have two people when drilling the holes - one person drills and the other should hold the plexiglass really, really well - if you let it pop up or down when drilling it can crack. i put both hands right next to the hole he was drilling and put almost all my body weight on the plexi so that it didn't crack.