The ALFA AWUS036H adapter is based on the Realtek RTL8187 chipset. The drivers should be built into Ubuntu, but you may want to try installing the latest from Realtek:
Download the "Linux driver for Kernel 3.0.0/3.1.0/3.2.0" from the Realtek website here.
It will open in Archive Manager; extract the rtl8187L_linux_1041.0209.2012 folder to your Downloads folder.
Open a terminal with Ctrl+Alt+T, and type/paste the following, one line a time:
sudo apt-get install build-essential linux-headers-`uname -r`
sudo make install
Then reboot, and your AWUS036H should be detected.
After the wifi connection seems more robust but only been a day so still evaluating.
But I go look into and clean my downloads folder. And can't delete the folder.
Shows a lock /home/orbmiser/Downloads/rtl8187L_linux_1041.0209.2012/rtl8187/.tmp_versions/r1871.mod file
And tried to delete the downloaded packages from downloads as have them backed up to another drive. And cannot delete the folder. Me thinks the procedure actually installed part of the final installed and in the downloads folder? Or something left over and how to delete it?