Many websites tell me effects of microgravity on the human body over a period of months. However nothing about the immediate effects of it. Could it be because there isn't any? I once read that fluid redistribution due to microgravity make you want to relieve yourself within two hours time.
Organic Marble, as usual, is correct in his answer, as far as it goes.
Anecdotally, I can add a few primary effects and one secondary effect to the list:
Fluid transfer to the head (a primary effect) is generally noted within minutes after the onset of microgravity conditions. It feels as if you are hanging upside down in Earth's gravity well and manifests itself as a feeling of fairly severe head stuffiness and sinus congestion. We referred to the phenomenon informally as "launch face." The externally visible effects seemed to remain for at least two weeks, but the uncomfortable feeling was generally mostly gone after the first 48-72 hours in said environment. I'm not sure if the externally visual effects ever go away - I've noticed that my friends who are serving long duration missions on the ISS seem to never quite get back to looking exactly as they do on Earth as long as they remain in Space.
Frequent urination (another primary, but acute effect) is generally noted within two hours or so after the onset of microgravity conditions. Because of this, some crewmembers will intentionally launch in a dehydrated state. However, I understood (in 2002) that this practice was discouraged by the NASA flight doctors. After about two days in Space, the body has achieved a new fluid equilibrium and urination frequencies stabilize to a "new normal."
A few words on spinal elongation (a primary effect mentioned by Organic Marble in his answer): For me, some lower back pain became evident after about four days into my mission. I'd say that over half of all Space Shuttle crewmembers complained of lower back pain during a mission. I used to sleep with my knees strapped to my chest - this seemed to keep my discomfort at bay. It was generally accepted, around the 2002 time frame, that said pain was directly related to spinal elongation.
A few words on space adaptation sickness (SAS) (a primary effect mentioned by Organic Marble in his answer): Anecdotally, it was acknowledged (2002 time-frame) that most crewmembers largely got past the effects of SAS by about day three or so in space. I was pretty "green" throughout day two, but felt much better during later days. However, not everyone was so lucky, notably Senator Jake Garn. As the referenced link states, the unit of SAS is jokingly referred to as a Garn. It was also said that the second-highest level of SAS affliction ever attained in the history of manned spaceflight barely registered as one nano-Garn!
Eye irritation (mostly a secondary effect, I believe), is noted by most crewmembers within a few hours after the onset of microgravity conditions. We believed (as of 2002) that this effect was caused primarily by dust and lint in the air. Although the Orbiter crew cabins were quite clean before launch, any particulate matter present, as well as lint displaced from crew clothing, remained suspended in the air until removed by air filters. I found this eye irritation to be moderately uncomfortable. Some crewmembers used eye drops to mitigate the discomfort. While this effect never quite went away for me during my 10 day mission, it didn't bother me too much after day two or so. However, I do remember that the eye discomfort was cumulative throughout a crew duty day and, by the time bedtime arrived, I was ready for some relief in the form of some "shut eye!"
One curiosity to add: My initial feeling after the onset of microgravity condition was not a feeling of zero-G, it was a overwhelming sensation of negative-G (i.e. I felt as if I were being drawn to the ceiling of the flight deck). Although several other NASA Astronauts I've spoken with had a similar experience, I can't comment as the the overall prevalence of this phenomenon.