My dick is clean and I don't piss on my hands so usually I don't find it necessary to wash after taking a piss.
After taking a dump I'll wash my hands, there might be a chance that a rough piece of corn or peas or some other fecal matter pierced the protection of the toilet paper. When washing after a shit, I use washing method #1, which is to turn on the hot water, and then while the water is running I dispense liquid soap on my dry hands and lather, then hold my hands under the now hot water and countiue rubbing until there is no trace of soap. Towel dry (at home) (air dry or blower dry if out). The soap I use is usually some kind of liquid soap that has some kind of flowery or herbal scent and anti-bacterial ingredients. Some people say that you should use some kind of moisturizing lotion after washing, but I don't... maybe you could poll the forum as to who uses lotion after washing?
After sex I'll wash my hands, face, pecker and ass. Since you only asked about hands I'll skip the face, pecker and ass washing techniques and save that information for another thread. I use a modified method #1 procedure when washing my hands after sex. I'll turn on the hot water and then while the water is running I dispense liquid soap on my dry hands and lather, then hold my hands under the now hot water but this time I won't rinse off all the soap completely (because I need to wash my face, pecker and ass).
After working outside, or on the car... I'll use method #2. Which is wipe hands with rag, then use waterless hand cleaner, then basically on to Method #1 to finish.
After working in the kitchen, I'll use Method #3. I'll run my hands under luke warm water, then a small drip of dish soap, lather, rinse till no more soap is on my hands.
I'm sure there are some great resources on the web about hand washing. Along with community groups that discuss important hand washing issues, I've never really looked into it or put much thought about my hand washing.