Easy EXP
Aside from random grinding throughout your adventures in Japan and EDEN, there is one base method that will allow you to easily obtain the tools needed for the advanced method quite early in the game. This method involves the OFFLINE Colosseum.
You can repeat every Cup in the OFFLINE Colosseum as long as you purposely lose during the final match, this will allow you to gain a lot of EXP in a short amount of time.
Once you understand the Base Method and are at least at the Gold Cup (Gold Cup unlocks at Chapter 6; after the Silver Cup is beat. Please see the link at the bottom of this page to be redirected to the Colosseum Cup List) you are ready to begin training via the Advanced Method; as the Gold Cup is the first of the cups to offer a average base EXP earned above 1k (without beating final round) of : 1,300; while still remaining relatively easy (Except for the final round Flamedramon).
There are 2 Digimon that have the Support Skill : Platinum Bonus; it DOUBLES earned EXP; these 2 Digimon are PlatinumSukamon (Champion) and PlatinumNumemon (Mega).
There is also an equippable item that increases EXP earned in battle (as long as the Digimon wearing the item are in battle when the battle ends). This is the Tactician USB; it stacks with itself and also with Platinum Bonus.
The Digimon
PlatinumSukamon has 2 equipment slots, and PlatinumNumemon has 3. The easiest way to obtain these digimon is as follows:
Motimon -> Hagurumon -> PlatinumSukamon -> Etemon -> PlatinumNumemon
You need to begin with Motimon as PlatinumSukamon requires a higher level than a newly hatched Hagurumon can provide.
Obtaining Tactician USB
The easiest way to obtain the Tactician USB (or rather an early game way to obtain 6 for 3 PlatinumSukamons/9 for 3 PlatinumNumemons) is via the DigiFarm. It is only obtainable via the Development command; for 1,000, NOT 10,000. The more Developer-Know-Hows you have in your farm the easier it will be; along with the more "Builder" type Digimon in the farm (especially the Leader) the faster the develop process will be.
Start developing and go about your Digi-business until around a minute before the time is up; this is crucial: SAVE. I personally reccommend saving multiple times every 5 seconds so if you do not get the desired item you can reload and try again without having to wait an extended period of time. The reason this works is because the recieved item from development is not known/set until you get the message in your DigiLine. You will recieve 2 Tactician USBs every time they develop it. After you get the items from the farm, start developing again and repeat process.
Bam! Super EXP Time
Equip the Tactician USBs to the Digimon (probably at this stage it will be PlatinumSukamon) and head to the Gold Cup. In battle I HIGHLY recommend you AutoBattle (press options button on your turn) so you can go fix yourself some tea or food, etc and only have to check back randomly to progress the rounds and AutoBattle again. If you have 3 PlatinumSukamons with just their regular moves and no others they MAY die if you AutoBattle, until you have 3 PlatinumNumemon's I would not recommend AutoBattling with the 3 EXP makers, just battle with 2 and a random digimon you want to battle with and have one EXP maker as backup in case by chance they get killed; as they have high DEF stats so it is unlikely. This way (2 PlatinumSukamons and 1 other Digimon also weilding a Tactician USB will net you around 28,000-33,000 PER fight in the Gold Cup.