When I did it, it consisted of listening to a fake call, entering the proper information in short time, then clicking on the correct resource to send to the emergency.
You'll have several things pop up at once, such as a caller giving their address, then a pop-up will say "Armed robbery" even though the caller is talking about a diabetic problem, and you'll have to click on the "Police" button, while still entering information.
Our center and others I've applied to use Criticall. You can Google it. It tests typing speed, memory, multitasking, etc. Sounds similar to what Linus took.
It depends on the agency and area. I know California has some weird specific certification process (go figure). Most are going to test typing speed, your ability to listen and multitask. If you can, learn how to 10 key.. Being able to type numbers quickly and accurately helps.
I dispatched for law enforcement in California. The only thing I did for our agency was to pass a typing test (net speed). They took care of all the training through the course of a year, breaking in on phones, mock calls and the like. Over the course of that year, phones were first and they gradually worked me into radio traffic. All with a senior dispatcher/trainer. Training also consisted of ride alongs with officers to get to know city geography and priorities.
I would also like to add that in addition to these tests which measure skills and recall, they are also evaluating how you carry/present yourself.
During the interview while talking with them, if you get excited or flustered or start talking real fast, that is a no no. Also, if you act somewhat shy and talk quietly or mumble...again another no no.
Present a confident, cheery attitude and speak to everyone in a controlled tone. Do not be a robot but keep emotions in check and enunciate all your words and speak clearly to everyone during the process.
While you most likely will not be on radios for any length of time, it is good to demonstrate your potential from day 1.