a) Increase sharpness and reduce blur.
use higher f-stops to get better sharpness
make sure your focus is spot-on
use higher shutter speeds to reduce blur
the catch here is that when the f-stop goes up, your shutter speed goes down, and vice versa. so the only way to keep both f-stop and shutterspeed up, while maintaining proper exposure, is to use flash or bump up your ISO
b) Take sharper images without a tripod.
use faster shutter speed, usually 1/x of the focal length you're shooting at. i.e. if you're shooting at 55mm, try to keep the shutterspeed above 1/60 or faster.
that being said, if you want to take sharp, clean, and blur-free night photos - use a STURDY tripod, turn off VR mode (Nikon VR doesn't like tripod too much... unlike Canon's IS), set your ISO low, up your F-stop, and use a remote or self-timer to release the shutter.
c) Speed up shutter speed via ISO setting.
you just answered yourself with your question.
high ISO = sensor is more sensitive to light = more light = faster shutter speed
d) Change the camera "mode" to the ideal setting.
i think the D5000 has "Scene modes" - those are usually dialed in to give you the best ideal settings for those type of situations. you can play around with those to see what the camera does with all the settings, under given circumstances, and then try to duplicate the same using one of the manual modes.
once you are more familar with how to adjust exposure settings, move away from scene modes and use one of the M A S P modes.
Also, ANY SLR camera will let you set your shutter speed, - it's the "S" mode on your top dial.
You'll most likely have to spend some time reading stuff online/books about the relationship between these 3 guys:
ISO
Shutterspeed
Aperture
once you understand them you'll be able to adjust those settings depending on different lighting circumstances.
Also, you'll most likely need to get some type of photo-editing software for your pics. A lot of the pics you see are heavily edited to bring out the contrast, color, and etc, so what you see posted isn't always what the camera saw when the pic was taken. I for one is not too into too much post-editing but I know many here use photoshop extensively to give their shots that "pop". *wait, you said you got photoshop. lol it's late and I'm sleepy*
You can set your Picture Controls settings to bump up in-camera processing for contrast, sharpness, and saturation. That way you can do the least amount of editing once the shots are taken.
Read the manual if you haven't already - it really helps you understand what each setting does and how you can use it.
Check out this Nikon site, it shows you the basics of your camera and how to use it :
http://www.nikondigitutor.com/index_eng.html pick your D5000 and go through the tutorial.
Check this site for detailed info on camera terms:
http://www.dpreview.com/learn/?/Glossary/