You earn medals by participating in Tours on Tortimer's Island. You can either do this solo, with friends, or through random matchmaking through the Internet.
The number of medals you are awarded is dependent on how well you do in each minigame. The better your performance, the more medals are rewarded. There are also 3 difficulties, from 1-3 stars, and the higher the difficulty, the more medals you earn.
For example, during the Easy Hammer Tour (1 star), I hit the machine 91 times, which gave me a Gold Tortimer award (these are bronze/silver/gold and aren't tangible, just an award to judge how well you did) and 6 medals. During the Level-Up Hammer Tour (2 stars), I hit the machine 80 times, which gave me a Gold Tortimer award and 8 medals.
In addition, when playing with multiple people, you earn Bonus Medals based on how well you did in comparison to them. The way the games work is that they are a mix of cooperative and competitive. You all have to do something that works towards a collective goal, but you do get bonuses based on how well you did. So, again using the Hammer Tour as an example, you have to hit the machine 30 times within 3 minutes. Each person's hit would go towards the total, but at the end, they would also get bonus medals for how many times they hit it.
Once you earn 50 medals, you can earn membership to "Club Tortimer", which allows you to participate in Tours with random people on the Internet. If you're not a member, you can only go on Tours with people with whom you are friends. This is handy if you don't have friends that you can play with or they're on at times when you're not available, etc.
In conclusion, the fastest way to earn medals is by playing with multiple people as opposed to solo, and playing on higher rather than lower difficulties (and performing well, to boot).
Other flesh and blood players can donate to public works projects, even people just visiting your town, not just other residents! Hope for rich friends!
Villagers do contribute towards public works projects, but the amount tends to be so negligible that you'll still end up paying for the majority of the project yourself. They do this automatically, and there's no dialogue option to engage or encourage them to do so.
Best Answer
Construction:
You should just be able to talk directly to him (Like click like you would talk to any other villager) and donate money towards it, up until its completion. It's not some collection bucket, he himself takes the money.
If you didn't actually choose and set a project you still have to do that first. Talk to Isabelle and then walk with her to pick a place to put the project if it requires. Then Lloid will sit at that location until it is completely funded. (Villagers hardly donate money, so it's up to you).
The quoted text is from the wiki.