As of right now, the best way to earn ms shards is just to interact with your professions, you can get... I think it's 25 shards a day (so 2.5ms if you really crack down and get them all). Very slow progress, but progress nevertheless.
Whole moonstones are largely given out through the achievements system, which is.... Mostly just done via playing the site, but there are several you have to go out of your way for. Not super reliable short term, but good for an occasional bonus. Don't obsessively check, the numbers get silly to get focused on, but check every week or so.
Den costs keep going up by 10 ms per (so 10 for one, 20 for the next, and so on), until the last den currently available is 90ms to unlock. :S
If you already have enough access to MS to print a CA token (100ms per token), selling CA (art tokens, basically, you pay the site to make apparel for it. You can print a certain amount of these with each token you buy) tends to print money. But it has a high overhead for someone new to LW to get into-- if you are willing to do preorders though, some people do that so they can afford the tokens to print in the first place. Full disclosure, I don't interact with the CA tokens or market at all-- I don't know if it's gotten at all harder to sell CA or not.