Gathering Moonstone shards and crafting Bone Paste is a very effective (albeit time consuming) way of saving up MS.
MS shards can be gotten via any of the playable features (cooking, campaign, fishing, etc), as well as from the Activities. You will need 10 total shards in order to be able to craft a MS.
You will also need 5 Bone Paste, which can be crafted with 3 Bones, which you can get from things like hunting, the Mole Market, Gauntlet, and Campaign.
It's a time consuming process, but it's the easiest way to get MS!
Yeah that's how I've been doing it, but I've had a hard time coming across the shards. Of two days of playing, where I've been playing for a good few hours in total, I've only managed to get 3 whole moonstones. I saw someone say you could get way more than that, but it seems impossible unless you want to spend the whole day doing it.
Cry because the exchange rate for P:MS keeps climbing up rapidly.
Basically just keep trying to get shards. Just doing stuff around the site like fishing, mining, pageant, etc nets me shards which I then craft. It is SUPER SLOW, but you will get there. Eventually.
Can also try writing or drawing for MS as well if that is something you're into.
A better idea then trying to gather shards would be to create an account on flight rising instead and use it to buy moonstones from other people. A lot of folks prefer offsite trading and it’s the fastest way to buy curency.
I’ve had lots of success grinding arena and quick selling the arena exclusive companions for like 100 MS off whatever was cheapest in Flea Market. It was was trying to save very very quickly though, so with a little more patience than me you could probably make a bit more off of them.