Yeah I've had a couple of suspect floaters in the beer before. I always make sure to work in a clean environment and sterilize and sanitize equipment to avoid infections. I've never encountered an infection before, but I'd almost be interested in doing a small batch and creating an infection intentionally just to gain the experience of knowing when in fact my beer does have one.
Cold crashing is simple, but requires you to place your Carboy into a fridge or freezer with a temp controller (So you don't freez the beer). You will drop the beer temp to 36f-40f for 24-48 hours. The cold temps will force anything in suspension to the bottom. As for the yeast, there will be plenty of yeast still in suspension for your bottling (assuming you bottle). Don't worry about allowing the beer to heat back up to room temp when you bottle, bottle it cold. If the beer heats back up, you will slowly start to see floaters such as krausen, hops, etc make their way back to the top.
In the event you bottle, use the same amount of priming sugar you normally would. I know the priming sugar calculators ask you for the temp of the beer. Don't put 38 degrees. Put the temp the beer was when primary fermentation was over (eg:68degrees).
Also, switch out your airlock to an Stype airlock. I fill mine with vodka or even Jameson. This style airlock will allow for pressure to go out of the carboy as it will also allow for pressure to go back inside. When you cold crash your beer, the carboy will want to suck back in and cave in. Just like you leaving a half consumed coke in the hot car for hours it would expand. Put it back in the fridge and it will go back to normal.
Hope this helps