Did you carbonate your cider? Anything that is bottle conditioned (carbonated in the bottle) will have sediment.
For uncarbonated ciders and wine, the answer is super simple. Time. With time, all the stuff that causes cloudiness (like suspended yeast and proteins) and haze settles out. I rack my wines and ciders about every 30-45 days, until no new sediment (called lees) settle out, then bottle (or sometimes I wait a year or so to bottle anyway). No sediment at all in any of my wines or ciders, and they are crystal clear, just like a commercial white wine.
You can purchase filtering equipment, but it is very expensive, and the cider/wine must be clear before filtering. The filtering does remove all yeast, though, so it really polishes it nicely. I don't filter, since I've heard that it can also strip flavor out of the wine.
I usually don't bottle any meads, wines, or ciders until they are about a year old. Sometimes older, sometimes younger, though depending on what it is.
Broken Leg Brewery
Giving beer a leg to stand on since 2006