Multiple options. One of the best things to do is to add a metal strainer at the bottom of your kettle to remove these particles before the wort enters the chiller, but some recipes require you to leave those in.
Most important thing to do is backflush the wort side with hot water after each use. This will knock most of gunk out before it ever becomes a serious clog. You will also want to sanitize it right before each use, either a lye bath, or pbw, or starsans. For most brewers these two steps alone will be all you ever need to do. We tend to use and prefer lye, but thats just because we already have several tons on hand for making biodiesel (where the diesel in DudaDiesel comes from). We carry 99+% lye for anyone looking for it:
http://www.dudadiesel.com/search.php?query="sodium+hydroxide" PBW and Starsans wont unclog the unit as well, but they sanitize just as well and are far safer.
If your wort is really hoppy, or youve just been using it for years on end, you will notice more permanent clogs which can be seen by the decreased output flowrate of your wort (the unit honeycombs with multiple fluid paths inside, so its near impossible to clog it to the point of it being unusable, but it can clog to where you lose efficiency). In this event you will first want to flush with a lye solution to break apart any oils or organics holding the chunks in, and then for the more serious protein pieces you will want to place your chiller in your oven and set it to self-cleaning mode for 2-3 hours and let everything simply burn out. One last wash with water can then remove the ash left inside.