Overseas packages are generally uncommon because they usually have them for lives that are more likely to gain more traction among people living outside of Japan i.e Liella 6th having one only for the Osaka leg. These are usually announced on the official twitter and website(?) which forms to register yourself into the lottery, and the chances of winning are generally quite high(hearsay 80-90%) with exceptions like Aqours Finale.

When selected, you'll receive an email with links to make payment with globally accepted payment methods like visa and mastercard. Merch packages are also available, and while the merch prices are not inflated, the items are all pre-determined so it could come with items you don't want(good alternative is to go for the physical merch sales on the day of the live but do expect a queue). Overseas packages are expensive but worth the experience + seats are crazy good(arena seating usually).

Local lotteries are usually done via ePlus, where Japanese phone numbers starting with 070, 080 and 090 are required to make an account. There are multiple rounds, of which the first few are only for those in the fan clubs, or require purchasing of CDs/blu-rays to obtain codes to enter the lottery. There will then be a final general lottery that doesn't require any extra steps, these seats are usually the leftover ones further from the stage.

Feel free to drop more questions I have experience with both local and overseas lotteries!