Bleeding trailer brakes is a hassle. I don't know which system type you have but first you need to locate the reservoir. It's generally a cap on top of the hitch just behind the latching mechanism. Once you find it, next critical item is to make sure the master cyl and reservoir is the highest point in the system. If you are parked with the trailer axles above the reservoir and master, it's going to be hard to bleed.
Once you have the master at the high point, the best tool to use is the vacuum bleeder kit;
http://www.craftsman.com/shc/s/p_10155_12602_00920930000P?sid=IDxBCM201410150001 or similar. Start by cracking the bleed nipples on each hub. We do this because they get corroded often and if you break one, you'll need to have a replacement before you start bleeding the system. If the bleed nipple doesn't move with modest torque, stop!
Do everything you can to avoid breaking off the nipple in the slave cyl. Clean it well, use PB blaster, then heat around the nipple to try and free it up. If you can't get it out, and it breaks, just do yourself a favor and replace the slave cylinder. You would spend hours trying to get the broken nipple out, and the slave cyl isn't that costly anyway. Hopefully you won't have any broken ones. Once it's loose, just snug it back up for a bit, and go back to the master reservoir. Using the vac tool, suck as much old fluid out of the reservoir as you can with a little hose on the bottle. Get all the old fluid out so you don't run it through the lines to the slave cyl. You'll likely get some rust along with the old fluid. Once you get the reservoir dry, put a bit of kereosene in there, swish it around, then suck that out. Clean the reservoir well, maybe do another kero flush.
Once the reservoir is clean, fill with the right fluid, which ever DOT it's rated for. Fill right up near the top of the fill port. Tap the side of the reservoir a bit to dislodge any bubbles around there. Go back to the furthest slave nipple, connect the vac hose to the nipple, open the nipple a few turns, and then start sucking the fluid through. If it's fairly cold, the fluid will still be viscous and move slow. Warmer days are better. Monitor the level in the reservoir and don't let it run dry, keep adding fluid as it goes down. Once you have clear fluid coming through, close than nipple and move to the other side, do the same thing. Don't let the reservoir run dry.
Now, if you had to replace a slave cyl, I would install it at this point, then leave the nipple open for a few hours and let the fluid gravity fill into the cyl. check the reservoir a few times, and never let it run dry. If you are lucky, gravity will fill the slave cyl. You can help it along with the vac bleeder.
Testing is hard because you need to get under the hitch, locate the master actuator shaft, and put a pry bar up in there and exercise it. Not knowing which system you have I can't give specifics on that, but it's best to get the master shaft moving a bit to look for leaks. You can also test it by driving, but it's hard to verify that it's working on both sides by driving and hitting the brakes.