> how do you get them to pose in such cute poses,
I don't - it's a matter of waiting until the bunny's in a cute pose, then snap. You just have to have the camera ready, and be able to grab the shot when it appears.
Sometimes you can get a rabbit to look alert by making a noise or saying their name or something like that. Sometimes you can anticipate when they're going to do something just by knowing the bunny.
> how do you get the picture to look like it was done by a professional?
Some of it's equipment, but really that's less important than it seems. Yes, a good DSLR will allow you to take pictures under marginal conditions where a cheaper camera might not, and for printed enlargements you can see the difference - but most of the time for web posts that's not a big factor. Unless the camera's so crummy that it just won't take good pictures, you should be able to get good shots with any decent digital. Ken Rockwell once wrote that the biggest thing a camera has to do is not get in the way of capturing the image you envisioned when you hit the shutter. If it can do that, everything else is technique.
I suppose the first thing is, "take lots of pictures, but don't post the ones which don't look good". It seems simplistic, but if you throw away the bad pictures, what's left is, on average, better. Learn to be heartless about it - if the picture's fuzzy, throw it out, even if you remember that the bunny looked really cute when you took the shot.
Second, learn to use your camera. Figure out what the controls are and what they do. Today's cameras do lots of things automatically - but don't just set the camera on "auto" and expect it to do everything for you. Learn how to set shutter speeds, change
focal lengths, or adjust apertures for
depth of field, or
how to use flash - or if the camera only allows you to change "scene modes", learn what the modes are and when to use them. It's not all that complicated, really. If you've got any questions, ask. That's what this Camera Corner is for.
Then, think about what the picture's going to look like before you take it. Andreas Feininger called this "visualization" in his books on creative photography (I have no idea if any of them are still in print, but if you can find them, they're priceless). Ansel Adams would sit and wait for hours until the light would be just what he'd imagined when he set up a shot. You're not going to do that in taking a shot of a bunny, obviously, but you can think, "this picture would be better if I moved a little left and got the overflowing trash pail out of the picture".
It may seem odd, but our brains are hard-wired to like some things visually. There are lots of rules about what makes one photograph better than another - "composition" - which in many cases are simply ways to make your pictures match what your brain expects to see.For example, people in Western cultures learn to read from left to right, so your eyes naturally "read" a picture the same way. Make your pictures flow in that direction. Don't center the subject every time - by the "rule of thirds", pictures look better with the subject on a "thirds line" (think of a tic-tac-toe board superimposed on the frame, and put the subject on one of the lines). Don't have anything in the picture leading your eyes out of the frame - your mind will try to follow, and it will look "wrong". Sure, photography's an art, and rules are made to be broken - but learn the rules first before you break them. For some examples, see
this thread.
Finally, don't post pictures right out of the camera. A lot of looking "professional" is properly processing the pictures you keep. Adjust the images so the blacks are black and the whites are white. Crop out things which distract from the image. Make sure the picture's level, not tilted. If there's a color cast, correct it. Remove red-eye. And so on... There are a number of threads in the Camera Corner which can help with that, like
this one about rabbits with red eyes.
Now, go take some pictures and share them with us!
Also, stay zoomed out further and crop the picture on your computer instead of trying to go all close unless you have a macro lens. That way you get clearer shots and don't cut off ears/tails/feet if they're moving. 
