Poodles need to be groomed at least every 4 to 6 weeks. They will need grooming their entire lives, so you should get your poodle used to it as early as possible. Keep in mind that you should not take your poodle to a groomer until they are up to date on all of their shots and no longer in danger of contracting anything serious or life threatening.
The type and brand of shampoo you use is entirely up to you. If you're sensitive to scents, you can use all natural scent free products. Keep in mind that their noses are much more sensitive than ours, so if a product has a strong scent to you it may cause them headaches.
Make sure temperature of the water isn't too hot.
The Ears must be cleaned. How you choose to do that is up to you, but be sure to keep water from going inside the ear canals.
Wash eye area to prevent gunky build up and tear staining*. (*Lighter colored poodles are prone to staining, but a proper diet will prevent that.)
Wash their privates. Even with short hair cuts your poodle may get poopy build up around their bums. If you're uncomfortable cleaning it with your hands, you can use a washcloth. If there are tiny poopy pieces, thoroughly wet the area and gently pull them off. You do not want any gross stuff there when it's time to use the clippers or it will get on them. Yuck!
After you've rinsed your poodle, make sure they are completely dry before attempting to clip any hair. You can use your personal hair dryer when they are little, but may find that you need a larger more professional dryer as they grow. Whichever drier you use, make sure you use low heat, and don't keep the dryer in one spot too long.