You can get a hose and a vacuum head, which can be attached to the suction side inside the intex pool or even to the skimmer itself (there's a part for that, but Intex is probably out of stock). Then you can vacuum with the pump/filter. But the fines might pass right through a standard intex filter (spun fiber) anyway.
Prior to getting a real vacuum (as noted above) we used this http://www.amazon.com/Water-Tech-BROOM- ... B0015UCRXM
very happily (with a thick opaque toddler stocking inside). I still use it now and again cuz the real vacuum is more of a PITA to hook up and mess with. For leaves, you can tuck the flap on the inside in so it sucks them up better. It works well, but the footprint is not very wide so it takes more passes to get all the floor dirt.
The above link to Amazon has a nice deal on this vac for $35. I'm pretty sure it's normally $99.
I've heard good stuff about some other vacuums too. Catfish rings a bell...
The hose vacuum is just terrible. Not only do fines pass through, it adds water to the pool, messing with chemistry. Blech!