A good trailer owner like you wants to make sure your trailer is well maintained. Checking the bearings is a part of that preventative maintenance. Here's how to it.
*disclaimer* follow the instructions on your axle manual, this is not a comprehensive guide, and may only apply to select axles.
Check to see if you need new bearings
Jack up your trailers so the wheels are off the ground. Make sure the jack is on the frame and not the axle.
Take the wheel and wiggle it back and forth to check how much play there is, or spin the wheel to see if it wobbles.
If there is any wobbling or wiggling, then your axle bearings need to be replaced.
Remove the Hub
Jack the trailer up
Remove the wheel
Remove the grease cap
Remove the spindle nut retainer
Remove the spindle nut
Remove the spindle wash
Remove the hub from the spindle
Pry the seal out of the hub with a screw driver or suitable tool. Do not drive it out.
Inspect and clean the bearings along with the spindle with a solvent and dry them.
Make sure to inspect the bearing inside the hub
Bearing Cup Replacement
Place the hub on a flat surface.
With a brass drift punch, tap around the diameter of the cup.
Tap in a new cup with the brass drift punch.
Putting it back together
Grease the bearing
Replace the seal and apply sealant
Tap the seal into place
Replace the hub bearings, washers, and spindle nuts
Rotate the hub assembly slowly while tightening the spindle nut to 50 foot pounds
Loosen the spindle nut to remove the torque
Rotate the spindle nut until snug
Cover with grease cap
Here's a great video on axle maintenance from Dexter.