This really does work. I made two of them and aimed at upstairs room, and it make a big impact on signal strength. Follow the simple directions here. This has been around for a long time, but it really does work.
As a ham and the little I understand about antenna theory I can tell you that this does not work. Here are the reasons:
1. The antenna on the router (which has a 2.1 dBi gain already since it is a half-wave dipole is partially behind the "dish." This kill much if all of the gain and makes the dish somewhat transparent.
2. Regular paper is not that reflective to RF I could ask the microwave guys at the radio club, but I doubt that the paper reflects the signal, this makes the dish opaque to the RF causing loss in one direction but not gain. You need foil to do this properly. Luckily combined with number 1 above the loss is a lot lower.
3. The design makes no attempt to focus the signal. Without 1 and 2 above the net effect would probably be loss, but combined with 1 and 2 above the net effect would probably be nil with a geeky look.
This post is not to make you not want to learn antenna theory and design your own antenna. In fact if you want to learn antenna theory just to prove me wrong on this in the case I am wrong, I encourage it. I encourage you to learn antenna theory anyway. Here are a few things to encourage you:
The 2.4 GHz band is a great playground for the unlicensed, you can have an effective radiated power of 4 watts referenced to an isotropic radiator. You can have up to one watt of transmitter power, but you must keep within the 4 watt EiRP rule. So with full legal transmitter power you can have 1 watt transmitter and a 6 dBi antenna and be legal. Just note that this does not account for coax losses. When dealing with microwave frequencies polarity does matter, you can lose up to 20 dB related to the other end with the opposite polarity (this does not come into power calculations). Note all rules are related to USA FCC regulations under 47CFR15.
Your first tip, when using a laptop lay your router antenna flat with the top pointing 90 degrees away from where your laptop will be. This could give you a net gain of up to 20 dB. Remember RF polarity is determined by the antenna system not any other part of the system.