The dust cap will install directly over the castle nut. You should be able to start installation of the dust cap with your hands by pressing it into the center of the hub. After it has been started, use a piece of wood to tap it in the rest of the way. Make sure the outer lip on the dust cap is tight against the hub or drum. The wood will help you to avoid damaging to the dust cap.
The main purpose of bearing protectors is to keep out water. A grease-filled hub will have some pressure built up inside, and this is what prevents water from seeping in. When filling the bearing protectors with grease, be careful not to overfill them. To help prevent overfilling, the bearing protector will have a small hole that allows the excess grease to spill out the side.
It is not a good idea to fill the hub with grease on every trip. If the release valve is clogged, or the hub runs out of room, the grease will probably blow out through the grease seal. If you have brakes on the trailer and the seal fails, the brake shoes will be contaminated and will need to be replaced.
It is good practice is to fill the hub until grease starts to move the pressure spring on the bearing protector. Check it to see whether the spring has gone down then add a little more. Bearing protectors come with bras (or covers) that are designed to keep the excess grease from flinging out of the release valve and help to keep your wheel clean.