You're going to get a lot of opinions on how and what to do.
If you'd prefer to keep it simple for your first weigh . . . at the very minimum, I would pull onto the scales and weigh everything (including yourself, passengers, and all your gear, water, propane, etc.). You want to replicate how your rig will be loaded if you were actually on the road. After pulling onto the scales, the weigh station should give you three readings: the weight on the 1) front and 2) rear axles of your TV (tow vehicle), and the weight on the 3) trailer's axles. Make sure the weight on each axle (front and rear) of your TV doesn't exceed the GAWR (gross axle weight rating) for EACH axle as shown on the door jam sticker of your TV. You'll also want to add the TV's front and rear axle weights together to make sure this number does not exceed the GVWR (gross vehicle weight rating) of your TV, also noted on the door jam sticker of your TV. Lastly, you'll want to make sure the weight on the trailer's axles don't exceed the trailer's total rated GAWR (usually noted on a sticker located on the left, front of the trailer).
Several posters have already given you some excellent advice on how to get even more detailed info. However, this is the minimum necessary to make sure you and your rig are safe.