Introduction
Trailer wheel bearings are the roller bearing type with a series of rollers in a cage. These roll inside a race or cup that is a strip of metal press fit into the hub. There is an inner bearing for the part of the hub towards the middle of the trailer axle and an outer bearing which is the one you see when you remove the nut under the dust cap. A grease seal is press fit into the hub over the inner bearing. The seal keeps bearing grease from leaking out of the hub onto the brake surfaces. Grease leaking past the outer bearing is controlled by a washer, nut, and dust cap.
The hub and bearing assembly slides onto a spindle attached to the axle with the grease seal on the inside and a washer and nut on the outside holding it in place.
Re-packing wheel bearings means removing the hub, pounding out the old grease seal, cleaning the bearings and hubs of all old grease. Cleaning the spindle, packing the cleaned bearings with new grease then 'slathering' all inside hub surfaces and the spindle with new grease (not too much) to help prevent rust, Then, reassembling the hub on the spindle with the right tension.
The standard recommendation is that you re-pack your trailer wheel bearings once a year. This is because trailers tend to sit a lot and that can contribute to condensation inside the wheel and that can lead to rust which, in turn, leads to particles which can score surfaces and cause friction and bearing failure. Re-packing the bearings also makes it easy to inspect your brakes and running gear in order to detect and fix potential problems before they become a hazard.
This is not that complicated or sophisticated a task and can easily be done by amateurs willing to wrestle with awkward and heavy tires and hubs. Plan on an hour or so for each wheel

Be sure to take appropriate safety measures. Set up in a level spot, with plenty of working room that is well-lit and free of dust and grit. Keep wheels chocked to limit any trailer motion. If using jacks to lift the trailer be sure to use jack stands as a backup. Eye protection will be needed. Plan ahead and plan for safety.
Tools
There is no real need for any special tools. The hub nut is so large a 12 inch crescent wrench may not open wide enough so water pump pliers may be used. This nut should never be much more than finger tight so the water pump pliers work just fine. Standard pliers are used to remove the cotter pin. Note: the cotter pin keeps the nut from rotating after it is set. A brass rod or socket extension or maybe even a screwdriver (in a pinch) is needed to reach through the hub so you can remove (pound) the old grease seal out of the hub. A small block of wood is needed to evenly pound the new grease seal into the hub. Diagonal cutters can be used to help trim the NEW cotter pin after installation.
If you don't like to get grease on your hands, use the latex gloves or pack bearings inside a clear plastic bag.
Don’t forget a trash can. You need a good-sized receptacle for grease-laden rags and old parts.
Supplies
The supplies you will need are paper towels or rags, cleaning fluid, and brake cleaner. Latex gloves might be nice to help keep your hands clean, too. The 1975 Airstream service manual suggests using kerosene as a cleaning fluid but what you use now may suffer environmental and safety concerns. Brake cleaner is an aerosol spray that you will need to clean off any grease that gets on brake surfaces. It is also makes for a good final cleaning step for the bearings. Rags or paper towels are needed to mop up all the old grease and do the initial cleaning.
You can use brake clean for a cleaning fluid. It is convenient and works very well to clean up whatever grease is left after wiping parts down with a rag but it may take about two or three cans per wheel. DO NOT use compressed air, there is a potential of the bearing spinning out of control causing it to shatter with tremendous force.
Parts
Hopefully the only parts you will need are grease seals and 1/8” x 2” cotter pins. Where you buy parts can make a big difference in how much you pay. When you go to get new parts be sure to take a sample of the old one with you because it usually has a part number or can be measured to make sure you get the proper replacement.
Grease should also be on your parts list. You can pick up a tub of basic trailer hub.
Bearings and races, if they need replacing, should be replaced as a set. These aren't that expensive but, again, that might depend upon your source. You can often find a complete package of inner and outer bearings and races with a seal and cotter pin. However, you may not know you need bearings until disassembly.
Set up
Set up you work area(s). One at the axle end with pliers and screwdriver and a place to set the lug nuts, cleanliness is imperative. For connivance set up another for cleaning and packing the bearings, and possibly a third for cleaning the hub that is sturdy enough to support a bit of pounding to get the grease seal in and out. Put a stool near the axle end so you can sit while working the lug nuts and moving the wheel and hub around. Hopefully the only pounding you will need to do will be to remove and install the grease seal. The proper tool would be a brass drift (rod) but screwdrivers can usually handle the light loads needed for the job of removing the seal. A block and hammer is all that is required to install a new seal. However, if you need to replace a bearing, you will need a decent drift to help you get the race for the bearing out of the hub and also to install the new race without doing damage to the race or hub.
Remove the wheel, store fasteners in a clean accessible area, it is preferred to put them in a clear plastic bag.

Cautions
Don't drop parts! You don't want to ding the bearings and you don't want to get any dust or grit into them as it might score surfaces.
Remove the Hub Dust cover by prying off with evenly with a flat screwdriver. Wipe clean then store in clear plastic bag.

The cotter pin should be bent around the retaining nut. Straighten and remove the retaining cotter pin. This may be re-used but a new pin is preferred. Remove nut and washer. (Counter clockwise)

Remove the hub by carefully pulling, by hand, off the brake assembly.

Remove the Bearing assembly by sliding it out of the hub.
Inspect carefully. After you clean everything thoroughly, carefully inspect the bearings and the races for rough spots, pits, or anything other than a nice shiny smooth surface. Any discoloration or roughness is an indication of trouble.
Clean grease from anywhere it shouldn't be. Make sure there is no hint of grease on any brake surfaces. This is critical.
Remove the Seal, if required, from the hub by carefully tapping with a brass rod.
Remove inner bearing assembly if required and clean as described above.
If you can not remove the inner bearing, wipe as much grease as possible from the bearing area.
Verify Clean and install the inner bearing and seal by placing the hub on a flat surface. ENSURE the bearing and seal enters the race evenly.
Slather the inner bearing assembly liberally with grease.
Utilizing the wood block gently tap the bearing into place. Utilizing the wood block gently tap the seal into place.
Take the opportunity to check other parts while you have the hub off. Clean the cobwebs or debris from the brake parts and check for wear. Check wires for good connections and good condition, no age cracking and bare or exposed areas. Make sure springs are attached to the brake shoes.
Carefully install the hub back over the brake shoes by gently pushing towards the trailer until seated.
Slather the outer bearing assembly liberally with grease. Install the bearing assembly onto the spindle and hub.
Tension carefully and check. When you tighten the nut down on the washer and outer bearing, don't be too aggressive. First make it pretty tight (some spec 20 ft lbs.) while turning the hub in order to seat the bearings. Then loosen the nut before taking it down snug until you get resistance with your wrench (or pliers) then back off a notch to where you can install the cotter pin. Note, the nut should be up against the bearing housing with little to no play. This should provide a few thousands of an inch worth of movement for the bearing housing. You can check after you get the tire on and lug nuts snug (but still off the ground). Grab the top of the tire and tug back and forth. You should hear and feel a slight thunk-thunk as you pull the tire back and forth but there should be very little noticeable play in the wheel.
Tighten lug nuts properly, typically 90 foot pounds, to set them to the proper manufacturers torque when you have lowered the wheel on the ground, and check them again after a few miles.
Do a follow-up check after a few miles on the road to make sure the lug nuts stay tight and the hub cool. Verify torque @ 90 Foot Pounds or manufacture recommendations.
Keep spares or at least specs - Some folks suggest keeping a spare set of parts in your toolkit. This may not be necessary but you should have part numbers for the grease seals, inner and outer bearings, and inner and outer races (or cones) in your trailer documentation set. Trailer places can probably pull the right parts off the wall just knowing the size, weight rating, and number of lugs on your hub but parts stores will want to look up numbers in their cross reference book.