(Update July 6, 2015: it appears Microsoft's online database now includes the latest INF file for this device which is from Realtek from 12/2009. So you may not need to go through the manual process outlined in the video. Try the following process first, then try the video if no luck: You must be connected to Internet first through internal Wi-Fi or Ethernet for this to work. Go to Device Manager, go to Other section, and right click "RT81787" device, and select Update Driver. Then select "Search Automatically for Updated Driver Software". Allow wizard to finish. Note this process will not work if you do not have Internet access through your internal Wi-Fi card or built-in Ethernet when doing it.)
We have tested the Alfa AWUS036H 1000mW long range WiFi USB adapter on Windows 8. There is also a range comparison to the on-board WiFi card at the end.
On our Toshiba notebook, it was plug and play, no driver needed. In this video we also show how to install the driver manually in case it is not plug and play for you (for this part, expand the video window or put in full screen mode to see on-screen text clearly). There is no official Windows 8 driver for this product yet, so this video details how to install using the Windows 7 driver. The Alfa Client Utility program is not currently compatible, but you can use the Windows 8 Connection Manager to scan for and connect to networks. Let us know in the comments section below if installation was also plug and play for you.
Update 11/15/2013: No video? No problem. Click here to see an online Windows 8 driver install guide for AWUS036H from Alfa Network, Inc. Note that this guide pertains to any Realtek RTL8187L based device from Alfa including AWUS036EW, UBDo-gt8, and Tube-U(G).
Update 7/13/2014: Several buyers have referenced they had an easier time doing the install by taking these steps:
1. Computer must already be connected to Internet using internal WiFi, then plug in AWUS036H adapter
2. Press Windows key + X key on Windows 8 desktop screen and select "Device Manager" from the popup menu
3. Under Network Adapters, click this device once to highlight, then right-click and select Update Driver Software
4. Cick "Search Automatically for updated driver software
This may not work for everyone.
Update 3/19/2016: Our staff and some customers have found that the above process also works for many Windows 10 PCs. Some customers have not had success so this should be seen as a possible solution and not a guarantee of Windows 10 compatibility.
Military and First Responder 
i installed successfully with your method but i still have yellow exclamation on the new installed driver :( not working.
ive done this before im not sure why it’s not working now??
good
I tried plug and play, chose windows 7, and it kept crashing. Your way worked perfectly. Thank you.
Mine works plug and play on a new HP laptop with Windows 8.1 64.
OK, after trying everything I could think of including this tutorial, I was about to give us when it dawned on me that I had it plugged into a USB 3.0 port. When I switched it out to a 2.0 port, it started working perfectly!!!