Exactly. I always keep a sponge / squeegee tool in my trunk, similar to the ones usually available at gas stations, so that I can wipe away any rogue drops of gas after filling up. People always look at me like I'm paranoid, but it pays off when I get to smile and nod at the owner of a less-than-ten-year-old-car with a rust patch below the gas door. I just dunk it in the nasty fluid they make available for cleaning your windshields (how is it by 10:00 in the morning, every container's liquid is already brown?), wipe the area, squeegee it off gently, and tie the sponge tool's head in a plastic shopping bag to keep it from getting my trunk wet. Every so often I rinse it out to keep from contaminating everyone's windshields with extremely diluted gas (hey, I wouldn't want someone else doing it to me!).
If I can find a spray or squirt container that won't leak, I'll start carrying a bit of water around too. That way it won't suck so much when there's no windshield fluid available at the station. Anything with a screw-on top (like a usual spray bottle) seems to magically come open in the trunk after a while. Apparently the two small toolkits (~100 pieces total, but they're life savers), roadside kit (jumper cables, crank-up flashlight, reflectors, etc.), and snow brush / ice scraper in the trunk are doing some screwing (well, unscrewing) while I'm not looking.
I don't drive anything fancy (currently a 2008 Fusion, previously a 2003 Malibu), but it's such an easy thing to do and it makes a world of difference over time.
Anyway, back to the OP:
You can sand it down with whatever you're comfortable with. A power tool of some kind with a wire attachment (drill, Dremel, or "dedicated" tool) will probably be the quickest, but it may jump on you and accidentally hit perfectly good paint if you aren't used to using them. If you have a junk car or even a piece of scrap metal or hard plastic to practice on (old steel wheels may work), try that first to test how steady your hand is. Otherwise, sand paper will be a LOT of manual labor, but it's hard to screw up.
Keep in mind you'll have to sand down a good amount of perfectly good-looking paint to really get the job done right (probably an inch of "good" paint outward from the area in all directions), since rust spots will often have pockets or "veins" running beneath nearby paint. It doesn't hurt to mask off a large area outside of the rust / nearby paint using masking or painters tape to keep from scuffing the clear coat if you go too fast with the sand paper and jump or miss. Chances are it will polish right out, by why make the extra work for yourself?
The key is not to rush anything. No, it won't look perfect, but if you do a half-assed job, you'll get half-assed results (rust returning in a year, etc.). Sand it down to metal, mask off nearby good paint with tape and newspaper, grab a "wide tip" spray can of primer (such as Duplicolor, the tip should be advertised on the back), spray a coat, sand it lightly if it looks uneven, spray again, etc. Black88GTA's suggestion of body filler will give the absolute best results, but it can be a pain to get right. If you notice any major pits in the metal after sanding it down, it may be necessary (do this before primer). If you've ever used drywall mud to patch a hole, Bondo is somewhat similar in concept. Apply it, run a scraper over it so it's smooth and matches the curve / lines of the body, and primer / paint.
Finally, when you've painted it and lightly sanded any drips / imperfections, you can clear coat it and machine or hand buff it to a shine. Read up on car restoration or detailing for advice, but keep in mind that even a cheap buffing compound or polish with hand buffing pad and some elbow grease will give decent results.
I realize that everything I've written may sound like a lot of work, but this is the way I'd do it. If you really don't care how the car comes out in the end (as long as it looks better than it currently does), do whatever you feel fit. It's a decent car, though, and it can definitely be turned into a fun project and a learning experience at the same time.