smokeywren

Find a load/inflation table for your exact size tire, and go by that. Weigh the truck on a certified truck scale so you know how much weight is on each pickup axle, divide that weight by two to get the approximate weight on each tire, then apply the load/inflation table.

Optional tires on 2011 F-150 FX4 SuperCrew were LT275/65R18. If that's the size tire you have, then here is the load/inflation table for that tire:

PSI . Weight (lbs)
35 .. 1940
40 .. 2130
45 .. 2310
50 .. 2535
55 .. 2660
60 .. 2825
65 .. 3000
70 .. 3150
75 .. 3305
80 .. 3415

Probably the most inflation you should ever need in the rear tires is 50 PSI. That's enough for 5,070 pounds on your rear axle, and your rGARW is probably less than 5,000 pounds. And the front ties will need less, so probably 40 or 45 PSI will be more than enough. Over-inflation results in a harsher ride and wearing out the center of the tread, with no benefits. So at most, use the load/inflation table plus not more than about 10 PSI. If the load/inflation table says 45 PSI, then don't inflate to more than 55 PSI.

If you have a different size tire, then go to the Toyo tires website and find the load/inflation table for your size tires. Tire brand makes no difference, so you can use the Toyo tables with confidence that they will apply to any tire of that exact type and size. Load/inflation tables for pickup tires are hard to find, but Toyo makes it easier.

There are two ways, and both work fine.

1] Go to a certified truck scale and weigh the wet and loaded rig - without the WD bars hooked up. Then drop the trailer and weigh just the pickup. Add the weight on the front and rear axles for each trip across the scale to get GVW of the truck. Subtract the GVW without the trailer from the GVW with the trailer, and the answer is tongue weight. If the scale is a CAT scale, the first trip across the scale will cost about $10, but the second trip across the scale will cost only $1 or $2.

2] Instead of going to a truck scale, I use a tongue weight scale. I use it often, so I bought my own and keep it in the trailer. It sounds like you probably need to invest in a tongue weight scale too. Here's my tongue weight scale:
http://www.etrailer.com/Tools/Sherline/5780.html