The issue with the genre of Random is that because it's so vast, it's difficult to give advice that will work with most books in the genre of Random. However I will try and give my best advice on writing introductions for Random books which can be challenging.
Unlike the prologue for a fiction book, your introduction doesn't need to be overly long or detailed, however you have to capture your reader's attention. You can do this by being humorous which people seem to enjoy when reading Random books. If you can make someone laugh by the introduction of your Random book, that person will most likely read on.
You need to explain briefly what your book is about, but in a way that entertains the reader.
Capturing the reader's attention from the introduction is important, so try and make the line really stand out by either making it funny or dramatic. Take my book called 'Irrational Fears', the first line of the introduction is:
'Is it possible to have a mid-life crisis at fifteen?'
That captures the reader's attention and is more interesting than me saying 'Hello, this book is about...'
Conciseness is the key!