The case starts in the morgue, as you use the Nunchuk to pan around the (glowing, blue, generally featureless) body, looking for abnormalities. In this case, that means slashed wrists and an odd puncture mark, both of which get stored in an inventory of sorts as clues. You can send inventory items to an assistant, "Little Guy," for analysis, and combine items to attempt to find connections between the two.
Then, we listened to previously recorded testimony from witnesses, pointing at individual statements in order to collect them as clues. Later, we were able to explore the victim's apartment, using the Nunchuk to move the camera and the pointer to inspect items and even spray Luminol to search for bloodstains.
Finding an important connection, corroborating a witness report, or deducing something about one of your clues (like, for example, that a knife you found was used to cause a wound on the victim) shows up as "Solid Evidence" and adds a star to that clue. Sometimes, you can deduce more information about evidence, by answering a multiple-choice question about it (complete with comedy choices). As you progress through the case, all the clues in your inventory start to be marked with more and more stars, giving you an indication that the case is nearing completion. Should you screw up any of this -- pick the wrong reasoning in a multiple-choice sequence, or focus on the wrong statement in a testimony -- you'll lose one of your limited supply of "hearts."
Atlus informed us that, while the events of all six doctors' stories in Trauma Team will follow a single timeline, you can choose to play them out of order. That is to say, if you want to play all six forensic cases in a row, you can do that and then move on, even if it means playing the story out of order. The menu for these cases reflects the actual in-game timeline to help you keep it straight.