Clairknowing is also known as Clairsentience, or "clear knowing"...meaning you just know the answers to something as if it comes from somewhere else, not you.
Clairaudience is my strongest "sense" and clairsentience is a close second. I'm not much of a "seer" in the sense that I see where things are, but I'll just know, you know? I ask a question and the answer just comes...I just know it. I won't say I'm right all of the time, but I usually am. I can't turn it on or off and sometimes doubt really screws up my perception of anything that comes to me, but clairsentience really comes in handy if I have to find something...lost items are shown to me (again I have to be in the right mindset - not too stressed and fairly open to anything) or I'll get the answer: "go to the [bedroom, car, under the table]." Sometimes I'll be given specific locations and other times I'll be given vague answers and I'll have to hunt for a minute but I end up finding what I'm looking for. That usually depends on how stressed I am to find something, especially if it's important.
Solutions to problems are sometimes given in this way - if you can't see your way out a dilemma just ask for possible solutions and write down whatever comes...
Intuition is more like a gut feeling or instinct. Clairsentience is knowing specific answers to specific questions. I use it alot when I'm doing card readings...I'll tell people what the cards are telling me, then I'll have them ask me questions. It's easier for me that way...
Being calm and having no worries/doubts that your abilities will or won't work is imperative. If I'm either bit stressed about something, that stress/worry seems to block information from getting through to my conscious mind. The answer to a question can come in many forms and you have to be open to anything you're given.
Hope this helps,
Nice, simple explanation here, so thought I would bump it up.