It seems that a lot of local travel agencies offers an excursion to the floating market that includes a visit to the tiger temple and other sighseeings. I'm only interested in going to the floating market. How to go there from Khao San? And which is the opening and closing time for this market? In the Wikitravel entry recommends to go to the Taling Chan Floating Market, is the same? or should I try to stay a weekend to enjoy this "at least somewhat authentic rural market"?
My first advice to you would be to NOT book a tour online. They try to upsell you - in this case, to the longer tour package including the Tiger Temple and the 'Bridge on the River Kwai' bridge - and more often than not it costs you a lot more too, because it's just the Internet middleman agency that keep a major share of the booking fee.
Go to Bangkok, and then most hostels do sell tours for just the floating markets, you can definitely find those and they are of course cheaper not only because it's shorter but also because buying it locally is much much cheaper than buying online. I believe there are a few floating markets around Bangkok so I'm not sure the specific one it's referring to.
For the other parts typically included in the itinerary, the Tiger Temple is in a VERY out-of-the-way place and hard to reach by public transport; in fact, I think I only saw tour groups being brought along. There's a lot of debate on whether what they're doing is ethical or not (and having visited the place I definitely think there's something shady about that place and how they operate) but then again it's not something you'll see anywhere else in the world - especially Western expat Buddhist 'monks' with more tattoos than the typical hardened escaped convict.
The other bit that's often included on the tours is the bridge that inspired the film The Bridge on the River Kwai in Kanchanaburi. I love that film, so I really wanted to visit that place too, and rather than a tour I'd recommend going there by train (as described on Seat61).. To be fair, if you haven't seen the film or are not a fan of it, it's not that exciting a place to go to, but train journeys on local trains are an excellent way to actually mingle with so-called 'real' locals.
EDIT: The hassle-free way to visit a floating market would be to take a tour...and it won't cost you that much. If you have more time, you could try making to the floating markets. Chances are, at some point you will have to take a taxi maybe and then it may end up costing you more than if you booked a tour. It's much more fun figuring it out yourself though, at least for me. I didn't try that in Thailand, I did in Cambodia. Cambodia's floating markets, to me, felt a lot less 'touristy' compared to Thailand's and loved the experience more. In Thailand, I found a lot of the shops were geared towards selling souvenirs and first-time travellers to Asia going through their 'Asia 101' course. That said, you can meet some interesting folks. Like this one woman at one of the floating markets near Bangkok (I'll need to check my journal to look up the exact name), she owns all the shops on one pier of the floating market. It's funny because you buy from any shop on that side of the pier and you get referred to her to make your payment (she still handles the tills on most days). Charming woman, talk to her if you go there, her picture will be on every shop sign so you'll know who she is.