How to reduce movement in photography?

I shot this photo with a Nikon D3300 and a tripod. Specs of this photo were 38mm, 20 second exposure, 13 f-stop. The lens i'm using is the 18-55mm kit lens. As you can see it is not very sharp. How can I prevent this? Should I get a different lens? If so, my budget is $200.

Did you use a remote shutter release to limit vibration? Which tripod, heavy sturdy one?

Maybe run some tests. Try again at various f-stops and focal lengths, adjusting for exposure. Put a sandbag on lower strut of tripod to make more solid. Put in manual focus of course at infinity.

The car streaks may be shorter but this is a test for sharpness.

And you need dry clear weather to limit the effects of moisture in the air - which can cause soft focus.

You don't need to spend any money on new lenses. Your problem is a technical one, not an equipment one.

Make sure your lens is focussed to infinity, then switch the lens to manual focus so it's fixed.

When you set your camera up on the tripod, make sure it's steady. Use the mirror up option on your camera, use a remote to fire the shutter, or use the self-timer so you don't have to touch the camera.

Image of cityscape time lapse, does appear blur exposed, but small copy here may not be clear due to size, link to original helps as well,
Before taking time extended shots, test with manuals settings on stills to figure out best reception of skyline, that may help with speed and focus,
Remote switch and having clear still air, maybe lower setting on manual,

http://annemckinnell.com/2013/12/15/best-lenses-for-landscape-photography/

http://digital-photography-school.com/7-tips-for-shooting-better-timelapse/

Either you were shooting through thick glass at an angle or you bumped your camera as evidenced by the double image. Either of those will degrade the sharpness. Your camera and lens combination is capable of taking sharp images.