When you start
Digimon World: Dusk, you choose to be a male or a female trainer and then you choose a pack to play with. This pack will be your first three digimon. You can choose from a balanced set, an attack set, a defense set, or a "pretty" set. Each of the different pack will have its own strengths and weaknesses. These are by no means the only digimon you can have, though. Each time you encounter a digimon in battle, you scan it. The higher your trainer level, the more data you will get on each scan. When you have 100% or more scanned, you can go digiconvert that data into a new digimon. Keep in mind though that you can only befriend 40 digimon at one time, so if you're trying to get specific ones for the quests or just because you want them, you need to plan in advance which ones you're training.
To train your digimon, you can either take them with you on your travels or you can leave them on a farm. You can have up to six digimon in your party at once, but only three active in battle. All six will get the experience from the battle, though. This can be used as a quick way to level up and digivolve your digimon. To train your digimon on farms, you first need to buy a farm (you will get a ticket for a free one after your first quest). You can own up to four farms at once. You can also enhance each farm with a terrain board and a BGM board. The different terrain boards increase specific species EXP. The different BGM boards change the growth rate for specific species. You can change out the terrain and BGM boards whenever you want, so you're not stuck with one once you choose it. You can also add goods to farms. You'll have to add food there. You can opt to add items to train your digimon stats.
Digimon World: Dusk consists of several different means of play. If you're one of those people that just wants to play start to finish and beat the game, you can do that in Digimon World: Dusk. It is quite possible to beat the game just doing all the main quests. You'll notice, though, that you're only 56% complete with the quests when you get to the end of the game. There are at least sixteen farm quests to do in addition to the main quests. When you take a quest, often times it warps you to a different starting point than normal. I did notice on one quest, I had to cancel the quest and go back to that world at the normal starting point so I could open a door to be able to get where I needed to go on the quest. Once you've opened doors/gates, they stay open.
There's a lot more to do, I don't have the space to cover it all. Make sure you do go to the Digi-coliseum and take the challenge to raise your trainer level as soon as you think you're ready. There's also DNA Digivolution, Armor Digivolution, Digi-Eggs, and many more things to work with.