Elementary,my dear Watson

Sherlock Holmes never said it. But when he solved the mysteries it always looked a easy and elementary job.
Didn't it ? That is the strength of observation and deduction. Holmes methodology as all the fans of the character will know were based on scientific analysis ,observation and deduction . Just by looking at the soil of the shoe of the person he could tell about the place from where he came. He could deduce(note the word) the past of the person just from the physical features of the person. He could judge the profession of the person looking at the shape of the hands.
"By a man's finger-nails, by his coat-sleeve, by his boots, by his trouser-knees, by the callosities of his forefinger and thumb, by his expression, by his shirt-cuff - By each of these things a man's calling is plainly revealed. That all united should fail to enlighten the competent inquirer in any case is almost inconceivable."
The following quotes demonstrates his belief in power of reasoning ,observation and scientific temperament.
"When you have eliminated all which is impossible, then whatever remains, however improbable, must be the truth."
"The world is full of obvious things which nobody by any chance ever observes."
"You see, but you do not observe."
"I never guess. It is a shocking habit -- destructive to the logical faculty"
"One true inference invariably suggests others."
Many times it was the simple observations and points that helped him solve the problems. For eg, in The Engineer's thumb he could fix the place of crime by observing that horse (for the horse carriage) used in the crime was fresh(ie had not gone for a ride). In other story from the observation that dogs didn't bark the concluded that the crime was done some acquaintance.
On the other hand stands the character of Miss Marple created by Agatha Christie. She was a old spinster. She was not a professional detective as SH but as good as anyone in the job. Whereas SH relied on scientific analysis for solving mysteries ,Miss Marple was helped by deep understanding of human characteristics. She studied the characteristics of her suspects to help her solve the problems. She was also a keen observer of human nature. So her methods employed more psychology and less science. Both SH and Miss Marple had the same aim ,to find out the truth about the crime but different approaches to solve them.