Mesprit
Mesprit is a Psychic-type Pokemon and is a part of the Legendary Psychic Trio of Sinnoh, along with Uxie and Azelf. Mesprit can be encountered at Lake Verity once you have defeated the Team Galactic Boss, Cyrus. At Lake Verity, Mesprit, Uxie and Azelf will appear, then quickly disappear, meaning that you will be able to encounter them in the wild. Unfortunately, since you cannot locate Mesprit on the map until you have encountered it, the initial encounter may take some time.
Masterball
Once you encounter Mesprit, you can catch it immediately if you use a Masterball. You receive the Masterball after defeating Cyrus so you should have one by the time you encounter Mesprit. To use the Masterball, select "Items" from the battle menu and select "PokeBalls." Select the "Masterball" and use it to catch Mesprit.
Mean Look/Quick Claw
One of the more popular methods to encounter a "roaming" Pokemon is to use a Pokemon that knows the battle move "Mean Look" in conjunction with a "Quick Claw" item. "Mean Look" prevents any Pokemon from running away and "Quick Claw" allows you to attack first, meaning that you can use it to prevent Mesprit from fleeing. The most popular Pokemon to use is Golbat as it's easily obtainable and learns "Mean Look" on its own.
Action Replay
If you own an Action Replay, you can also input a code that will immediately place Mesprit into your party. This code can be found online at various websites such as GameFAQS or SuperCheats. To use the Action Replay, you simply insert the "Pokemon Platinum" game cartridge into the Action Replay device and insert the device into the DS. Then you turn the system on, input the code and press start. Once you start the game, Mesprit will be in your party or in your PC, depending on the code.