1. Drains should flow downhill (The three rules of a journeyman plumber, 1. Drains flow downhill 2. Don't pick your teeth and 3. Pay day is on Friday). The downhill motion of the water creates turbulence; turbulence causes erosion of the grease and sludge in the pipe. Therefore downhill drain systems under normal use are self cleaning.
2. Main sewer should be at least 4" in diameter for most residential houses. Inside drains to toilets should be at least 3". Shower and floor drains should be at least 2". Kitchen sink lines should be at least 1.5". Bathroom sink lines should be at least 1.25". Bathtub drains should be at least 1.5" Clothes washer drain lines should be at least 2".
3. Plumbing systems must be vented. Air must be allowed to circulate throughout the system. When water is added to a closed system the air pressure would increase and sewer gas can bubble out the fixtures. A vent allows the air added to the system to push out of the system and make way for the waste water. Mechanical vents (sometimes referred to as Studor Vents, which is a brand of mechanical vents) are to only be used for situations where a vacuum situation is occurring and air needs to be let into the system. Waste water flowing down a drain system can potential create a vacuum in the line and suck the water out of the p-trap of a fixture. Then letting sewer gas in the system. Mechanical vents can only be used if the system has a fresh air vent somewhere in the system. Mechanical vents can never be used a sewage ejector basin.
4. P-traps are mainly used to prevent sewer gas from coming back into the house, however, they also prevent sewer flies and rodents from entering the structure. Toilets have a built in trap in the porcelain. All other fixtures have traps installed by the plumber. Sewer gas entering a house can be deadly since it is explosive, it also can carry disease.