In order to get medals, you will firstly need access to the Fugo Estate in Liberdam, which you can get by completing Fugo quests in the Adventurers guild, which after a few they'll notice you and invite you in.
You can win medals from games (very little amounts) or just buy them in the dozens, if you want to buy them it will cost you 625,000 total Gea to gain 100,000 Medals, but you only need to have 100,000 on you at one time, so there's no rush as if you're going for the platinum, Gea will become VERY easy to obtain.