So, I made the decision to finally learn how to read Katakana after another helpless night out without being able to read the menu - and after a very helpful friend pointed out that nearly everything on the menu is just English words written in Katakana.
So the next day, I started by learning how to write the characters using the lessons on this page - I learn best when I write stuff down, so this was an obvious first step for me. The page has detailed instructions how to write the characters, particularly when it comes to the order and direction of the single strokes. So for each new character, I wrote down one or two lines to practice. This looked pretty awful - and probably not very Japanese - at the beginning, but I believe I got better at it after I was about halfway through. Check it out:
In parallel to that, after each new block of five Katakana, I practiced recognizing them using this page. This is actually a great tool, as you can pick exactly which Katakana you want to practice, and you can also choose between different typefaces (some of them still confuse me now... but I'm working on it).
I also picked the correct pronunciation off of this page.
Finally, to apply my knowledge, I used the Google image search to find pictures of actual Japanese (drink) menus. If you want to try, just use ドリンクメニュー (pronounced dorinku menyu) as search term. And - holy shit - this actually works!
Although I am still very slow at reading, I seem to have them all memorized - within one weekend! I had expected this to take a lot longer. Now when I go out next time, I can at least make an informed choice as to what I should drink - hooray!
