Where do i clam?
Go to Bibiki Bay (needs CoP) and take the boat on the island route (there are 3 routes, only one goes to the Island). Once on the island speak to the nearby Mithra standing on the beach and get to it! For a fee of 500g per attempt, she will loan you her bucket.

How do i clam?
Once you have the bucket, explore all beachy areas of the island, where clam points always exist. Once you find one simply take action on it and obtain a random item.
Clam Points don't vanish like other types of harvesting, rather they are always there but are useless for 10 seconds after they've been harvested.

What are the rules?
Your Bucket can only hold '50pz' of items, each item has a set weight. If you surpass the limit, your bucket will break and all your items will be lost. You will have to pay 500g to try again. However, handing her a bucket with 45-50pz worth, the Mithra will offer to upgrade your bucket to 100 capacity for free. You can then go on to get 50pz more of items. If you now go past 100pz your bucket will break and you lose it all, including the 100pz limit. This upgrading strategy goes on to 150pz, and 200pz limit upgrades.

Once you're satisfied with your gathered items, simply tell the mithra you're done, and she'll hand over everything you've obtained. Note that if you have an upgraded bucket, your limit will return to 50 in this case as well.