I attended a dispatch assessment day earlier this year and, as mentioned already, there are two assessments: a dispatch concentration test and a rules acquisition aptitude test. There is also a colour blindness test.
The concentration test involves listening to an audio recording of a fictional station environment. Prior to starting the test, you'll listen to three sounds in order, two of which are someone saying "train ready to depart" and a whistle (I can't remember what the third sound was!). Make sure you memorise that order. You'll then listen to 50 audio recordings and, after each one, mark on a sheet of paper whether it is safe for the train to depart, dependent on if the correct sounds were heard and the order was correct. In addition, whilst listening for the sounds, you'll have passengers asking questions, e.g. what is the next station. You'll be given a sheet of paper which has all the information you'll need to answer these questions (including a fictional route diagram), and you'll mark the answer down on paper by marking a multiple choice box. I know this can sound quite confusing, but there should be example questions beforehand to ensure you know what you're doing, and there will be time to ask questions if you're unsure. This test can be difficult and can become a little arduous towards the end, but as long as you focus on what you're doing to the best of your ability, it is perfectly passable

The questions can come quite fast, so if you end up missing one (as I did once or twice!) don't panic and just try to regain focus for the next one.
The Rules Acquisition Aptitude Test (RAAT) involves reading a passage of text and answering multiple choice questions based on the content. There isn't really much advice I can give for this one, other than take your time to ensure you've read the passage properly. I believe there are some example assessments for this online, so it may be worth taking a look beforehand if you can.
If you pass both of these, you'll be invited to an interview which for me was on the same day as the assessments.
Best of luck with your assessment day and, if you have any questions, feel free to ask!