Watch the video above for a nice description of what needs to be done to make a DIY laminar flow water fountain on the cheap. There are lots of different DIY designs and ideas from the community that are variations on this idea. See other ideas below.
Kanal von Magicmastera has made quite a few videos documenting his Laminar Flow Water Fountain build process. The installation and effects of his final design look great! He designed a great cutter mechanism which lets the stream get stopped and started smoothly with just a small disruption to the straight flow.
 Luckydon1955 has put together a video showing the steps he took to make his laminar flow fountain. The built looks very nice and should last a long time. He has also added some RGB lighting to his stream, looks like his dog must love the new toy!
Zacharysc100 has made these two videos which demonstrate his DIY Laminar Flow Water Fountains construction method. He has put some serious thought into his design. Drinking straws like the others are his main weapon to make good flow.
Portojbc has made quite a few videos showing how his build works. The video above shows how his cutter works. He uses two solenoids to pull the cutter in and out of the water stream quickly. The results are quite good.