Asakusa is best known for its famous Senso-ji temple. I've chosen to focus on this one to deal with the famous and heavily visited Tokyo district, which I've never been able to enjoy as much as others (eg the west of the capital). Its foil and very commercial side gives it little authenticity in my opinion.
Starting with the long shopping avenue, which joins the majestic Kaminari-mon gate to the temple's main building. For centuries they say, businesses have sold their stuff at high prices. Accustomed to seeing hordes of tourists (mostly from China and Korea) all year long, no wonder traders are generally more unpleasant than elsewhere in Japan.
And then there is this amazing "jinrikisha" proposal, rickshaws for which you'll be charged up to 9,000 Yen per half-hour! Besides, it must be quite unpleasant to be transported in such an urban environment.
As for Senso-ji pagodas and buildings, I must admit the reconstruction post World War II with its maintenance and lighting, if untraditional, has the merit of offering a very postcard view of Tokyo.
However, Asakusa isn't limited to Sensoji Temple and other attractions are there to capture your attention, such as Asahi beer Museum and "Golden Flame" sculpture designed by Philippe Starck. I also really enjoy Sumida Park, named after the river. If you can, plan to visit Asakusa by bike and try to get lost in the small side streets, it's much more fun and you'll probably make awesome discoveries.
Asakusa photo gallery
Things to do in Asakusa
Asakusa by Kanpai community
Must see around: Tokyo attractions
By subway -- Tokyo Metro Ginza and Asakusa lines, Asakusa station (A18 or G19)
By train -- several lines of Tobu company
Warning: Asakusa is not served by the Yamanote line!
Allow half a day to a full day depending on what you want to see
Official page on JNTO (in English)