Shoturtle and Sarah have given 1/4 of the information on getting image separation, but I don't want you to be incredibly disappointed (which is possible with out the full picture on the creation of a shallow depth of field).
I've posted this a few times so make no apologies for just copying it
There are 3 main areas to getting a shallow depth of field (dof).
Focal length - the longer the lens the shallower the dof.
Aperture - the wider the aperture (lower f number) the shallower the dof.
Distance from camera to subject - the closer to the camera the shallower the dof.
So ideal situations would be long lens, wide aperture and subject close to the camera.
There is another contributing factor, not to dof, but blurred background and that is getting the background as far from the subject as possible.
Looking at the shots that Shoturtle supplied they are of a small subject so you can get closer/use a longer lens to give the framing. As we see from the above this will really decrease the dof so there will be much more isolation. If you were shooting a person then as they are much larger you have to use a wider lens/be further away so the dof is much much deeper.
Now, this next part is where you get some major differences when talking about cameras such as the FZ35 and you could be disappointed if you only thought that you needed the background further away.
Due to the small size of the sensor in a camera like the FZ35 the lenses used are pretty short. Yes they give a similar view to a long lens on a dSLR but as is not actually long (it's focal length) then it is really hard to get a shallow dof for anything other than thight head shots and even then it isn't much.
I don't want this to get too confusing but I also don't want you to make a decision that you are not happy with.
Let us take some real world shooting situations. A nice focal length on a normal dSLR is 50mm when taking portraits. This will give the same field of view as 14.1mm on the FZ35. OK, it doesn't matter if you are fully following the numbers at this point, but what is important is how they are going to translate to the amount of subject that is in focus and where it starts to drop off.
we can easily see how much is in focus before and after the subject.
I've assumed 8 feet for the distance but you can go and play with the settings on the calculator if you like.
With the dSLR with a 50mm lens, and assuming it is a kit on so you have f5.6 you get the following results.
Depth of field Near limit 7.22 ft Far limit 8.97 ft Total 1.75 ft
Anything outside of this is considered not acceptably sharp.
With the FZ35 in the same situation with the lens at 14.1mm and f4 (you might be able to go just wider than that but I wanted to give real numbers that I knew were possible).
Depth of field Near limit 6.43 ft Far limit 10.6 ft Total 4.15 ft
So, instantly it can be seen that there is a big difference, but this is not all of the story. As when you get outside of the sharp area how fast the rest goes out of focus as you get further away is also at a similar ratio, so you really do struggle with small cameras to get the desired results of a shallow dof/separation from the background.
As the 50mm f1.8 lens was mentioned here is what happens using that lens in the same environment at f1.8.
Depth of field Near limit 7.74 ft Far limit 8.28 ft Total 0.55 ft
So back to reality, if you want a human subject with a blurred background then you will only be able to get a this with a dSLR. Yes you can get some reduced dof with the FZ35 but only on the tight head shots and to really see the effect you want the background a long way away.
Hope that helps to clear up the confusion and assist in the decision for your needs.
Play around with the calculator and see what happens when the subject is closer, you use a longer lens, the aperture is wider etc as it can help get a better picture of what is going on. Remember althought the FZ35 says 27-486mm this is the equivalent focal length related to 35mm film and often causes confusion for situations like this. The actual focal length of the lens is 4.8mm to 86.4mm.
If you want to read a bit around this subject check out http://forums.steves-digicams.com/ge...op-factor.html