Sherlock Holmes is an ex Scotland Yard consultant, who moved to the states at some point and was checked into rehab by his father due to a drug addiction (no specifics, although as the original Holmes's vice was cocaine for a while, it is natural to assume that is what it was). An undetermined amount of time later ex-surgeon Joan Watson was hired by his father to be Holmes's live-in watchdog to make sure he stays on the straight and narrow, a period of time that they state as six weeks. Holmes breaks out of rehab on the day he was supposed to be released because he was bored, has someone "over" before explaining to Watson that he's returning to his freelance detective work with the LAPD and is heading to a crime scene.
All in all that summarizes the plot of the pilot without giving away any spoilers (as usual). Apparently Tobias Gregson was a minor character in the original series and not the top-dog detective in-charge but that's just a fun fact.
Anyways, Elementary is a must-watch for mystery lovers and Homes fans alike, I give it a 10.1* rating, this is by far one of the best shows debuting this season and I have high hopes for it, they recreated Holmes perfectly and Watson is given a more modern and American tone to contrast to Holmes's distinct Britishness.
Do I recommend it? Yes, most definitely.