All chimneys need regular cleaning, whether you burn wood or not, some more often than others depending on how they're used etc.
If you're able to get on the roof to sweep the chimney from the top safely, you can sweep from the top down, which can be easier sometimes, or if you think the chimney's got a more serious build-up, you can make something that works like the chimney ball you describe (if it's not so serious, you could alternatively use a burlap sack with some chains inside it in the same way I'm about to explain, for instance; holly bushes were a traditional alternative!).
The following assumes the chimney is straightforward in design and doesn't have any kinks in it, in which case I wouldn't recommend it at all and suggest you call in a chimney sweep. I also wouldn't recommend it if the inside of your chimney's degraded, as you risk taking off internal mortar or even dislodging internal brickwork, possibly giving yourself major and potentially expensive problems.
Take whatever precautions you need to stop soot engulfing the room from the fireplace (we have a stove, and it's enough to just remove the throatplate and shut the door).
Get a building brick (the type with up to three holes all the way through). Wrap it in some chicken wire, just enough to envelop the brick with a little overlap, then tie a decent length of rope securely through one of the holes toward one end, binding the chicken wire together as neatly as you can at the top.
Leave the fire unlit for long enough to let the chimney cool down, so it doesn't damage the rope and lose you the brick!
Assuming the chimney's wide enough to lower a brick down (I can't imagine many aren't unless they're stove pipes), you can compress the chicken wire around the brick so it fits snugly but not tightly down the chimney. Lower it gradually, working it steadily up and down as you go to dislodge the crusted-on creosote and soot.
If you encounter an obstruction, take it easy - you may simply have dislodged a bunch of creosote shards that have gathered towards the bottom of the chimney, and there's a danger of tamping that down into a hard pack that you may have problems shifting if you compress it too much. Otherwise, suspect a chimney kink or ledge you didn't know about, or possibly chimney damage.
Once you reckon you've cleared the length of chimney, if it's an old chimney and has only ever been cleaned by brushing, you may be astonished by the amount of debris that comes out of the bottom.
I strongly recommend following this up by rodding or sweeping the chimney with a brush from the bottom, which should clear any collections of debris that might otherwise block the bottom part of the chimney, or could catch fire the first time you start a proper fire again.
Finally, do a smoke test - burn a little paper and maybe something that will produce a short burst of smoke (say some leaves, but not too much in case you have a problem), and see if the draw is satisfactory and smoke readily clears the chimney top. If not, you may still have a partial blockage, so you'll need to run the brush up again.
Don't light the fire again till you're absolutely sure you have a good draw.
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