The Single Paradiddle, commonly referred to as just a paradiddle, is one the most popular rudiments. This, along with all the other rudiments is built on pairing singles and doubles: You alternate once, then double ( RL RR or LR LL). Also note that 'Diddle' is another word for, and means the same things as 'Double'. In all the diddle rudiments, the name will tell you how many times to single before playing the double (single RL, double RL RL, triple RL RL RL). The name can also help you remember the sticking: 'Para' lining up with the RL and 'Diddle' lining up with the RR. Saying it along as you play can be a huge aid in accuracy.
Learning to play a paradiddle smoothly, with and without accents will give your hands a huge amount of freedom in beats and fills. Memorize it, and make it a point to master this essential rudiment.
The Double Paradiddle is built off of the single paradiddle. You alternate twice and then double. Since this rudiment ends up in groups of 6's, it gives it a feeling of swing/jazz. Just like the single paradiddle, you can say it while you play it: 'Para-Para' (RL RL) 'Diddle' (RR).
The Triple Paradiddle continues to build on this rudiment and uses 3 sets of alterning and then a double. This will give you an 8 note pattern and feel a bit more square. Again use the name to help you remember the correct sticking: 'Para-Para-Para' (RL RL RL) 'Diddle' (RR).
The Single Paradiddle-Diddle uses the same building blocks as the other diddle rudiments, in a slightly different combination. You alternate once, and double twice (RL RR LL). This mean the pattern won't switch hands each time, so you'll need to practice your R and L leads separately. Use the name like all the others to help you get the correct sticking: 'Para' (RL) 'Diddle-Diddle' (RR LL).