Juggling 3 clubs is a lot like juggling 3 balls only it's harder and there's more stuff that can go wrong. They also hurt more. Before even starting with 3 clubs you should be decent with 3 balls, able to start and stop at will and keep a pattern going for at least a minute. Then you also need to have some clubs.
Before we start making throws, a few thoughts on holding a club. You want to grab the club somewhat in the middle just below the thick part. (see picture)
For some tricks you want to be down near the knob but not for the basic juggling pattern.
When you throw a club you also don't have to spin it much if at all, simply opening your hand to release it should give you all you need.
Pay close attention to where the catch is being made. As in all juggling accurate throws are more important than great catches. If you find you're moving your catching hand up or down, left or right, or forward or back to make a catch, your throw is bad. Spend a few minutes tossing a club from hand to hand, letting it make a single spin each time. Try to find the height to throw to that naturally gives you one full spin.
Once you're comfortable with the feel of a single club try 2 balls and one club in a 3 ball pattern. Place 2 balls in one hand and the club in the other. Throw a ball first and then the club as the second throw, if all went well throw the 3rd ball next and keep the pattern going. You might find the club takes more time in the air than the balls and your rhythm slows down to give the club time to spin, this is much better than trying to speed the club up to match the balls timing. So slow down for your clubs.
2 clubs & 1 ball is much harder than 3 clubs so the next step is 3 clubs. If you're comfortable with 2 balls & 1 club, 3 won't be too hard. The tough part is starting.
Place the first club in your hand, then lay the second club on top of that and hold it with the tips of your thumb, middle and forefinger. The knob of the second club should be closer to your elbow than the first club like the green clubs.
If you do it the other way like the red clubs there's a tendency to catch the knob when you start. Some people like to start with the clubs held like the red ones but I recommend the green. Try both and see what happens.
Another chance for pain is when you stop and catch 2 clubs in one hand, watch out for getting a fingertip squeezed between two handles. This is a mistake most folks only make a few times.
Okay, that should get you started.