This is just my personal account. Some of this information is in other thread, but I went through this personally.
Speak to the Nomad Moogle (After completing limit break I think) in Ru'Lude.
Come back to him with 15 merit points to complete the quest and activate the merit category.
You can only merit weapon skills which are available to your current job. Each WS costs 10 merits to activate initially. 10 > 15 > 20 > 25 > 30 or 100 merits total to max one out. Category has max of 15 points (Thus allowing you to get all weapon skills and level 2 in one of them, or max out three of them)
Each level increases the stat mod on the weapon skill by 17%. Apparently (this I heard from a friend; The weaponskills themselves are bugged on the english client only and appear as "." and do not function), they have a 15% base stat mod, which means that when maxed, the stat mod is 100% of the relevant stat.
(special obvious note: Apex Arrow is available to SAM without subbing RNG- finally a native archery WS on the job. All weapon skills are available on all of the listed jobs in the merit window natively and require no subs)
I cannot give any details on the WS themselves because they're bugged on my (every English?) client, but you can see the other thread for people who can test with the other clients.
(edit)I suppose this thread is redundant, but in case you don't want to sift through that really long thread, there's the basics for you.