We complete trials for linkshell members after they have met certain requirements (reasonable attendance, member for a decent amount of time). Once you've been told to pick a trial for a particular round, you can choose any single Magian trial, at least as of level 90. These can be 50 or 75 item trials.

You also have the option of picking an AF3+2 set of armor for a particular job in lieu of a weapon trial. If you pick this, you'll get all +1 seals, +2 items, and base feet.