The ESO Weekly Trial and Weekly Solo Challenge is usually different on each megaserver, however there may be times when they overlap and more than one megaserver has the same weekly at the same time. Currently, the following 12 player trials can appear as the weekly trial in the Elder Scrolls Online:

In addition, the following four player arenas can appear as the weekly trial:

As for the weekly solo challenge, there are currently only two possible locations for this:

That's a lot of DLC, but remember that you can access everything apart from the most recent expansion by having an active ESO Plus subscription. To improve your chances of getting onto the weekly trials leaderboard, it's best to find a coordinated team to play with, and joining a trials guild is your best bet for that. Score is allocated based on how quickly you completed the trial, how many player deaths occured, and whether you did the hardmode or not (some trials have multiple hardmodes, and the score will be higher the more of them you managed to do). 

For both the weekly trial and the weekly solo challenge, you can boost your performance and your score by making sure you are using a good PvE build for whatever role and class you are playing. We have builds for all classes and all roles that you can check out here.