Braden first off let me take this opportunity to welcome you to the forum.
Here is what I know (or what I think I know):
To clean between shots, use a spit patch or a lightly lubed patch, then a dry patch.
To clean between shots I do not really suggest spit. It will work and does work. I just do not use it. If it is a inline rifle I use a 50/50 mix of isopropyl alcohol and car windshield washer fluid. Lightly dampen the patch and work that from muzzle to breech in short strokes. This will help you clean better and lessen the chance of the patch getting stuck in the barrel. I would never suggest using any kind of lube to clean the barrel. Some solvents also work well. The reason I use the 50/50 mix is it cleans, is cheap to make up, and drys faster then some other things. After you have the barrel swabbed then a couple dry patches and you should be ready to load again.
To clean at the end of the season, clean thoroughly with soap and hot water, or whatever solution that you use. Make sure barrel is dry, run some dry patches, then lube with gun oil. Store barrel down.
At the end of the season after you have cleaned the rifle well and make sure it is nice and dry, then lube the barrel with a oil patch. You do not have to store them barrel down although many do. Also, if your rifle uses a hammer striker spring system it is sometimes a good idea to remove the spring, breech plug, and hammer. Put all that in a plastic zip lock bag and then tie that bag to the trigger guard. That way you have all the stuff together and the spring is not under tension. Also it is easier to swab the barrel out.
THings that I do not know:
When you are ready to shoot again the next season, what do you do? Run a few dry patches through, or do you need to wash out the barrel again?
When your ready to shoot again, take a patch and dampen it with your bore swabbing solution. Swab the barrel just like you would out in the field. Then follow that by a few dry patches. If the rifle is assembled, push a dry patch to the bottom of the breech and pop a 209 primer through the breech plug. This will clean and clear the breech plug. When you pull that dry patch back out off the breech plug you can check it. It should be burned badly. That means the fire is coming through the plug and you are ready to load.
How do you clean at the end of the hunt (when you will use it the next week)? Do you do the same as the end of the year routine? Or just run a few patches with cleaner, then dry patch, then gun oil?
At the end of the day there are a few schools of thought. If you have hunted but not fired the weapon, you can leave it loaded. Many people do that with good results. I have never had good results doing that.
I personally do not do that. I fire mine off. I then take the swab solution and swab the barrel extra good clean of fowling. Then some dry patches and finally oil the barrel. I will some times break the rifle down and actually clean it like at the end of the year.
Remember the kind of powder you shoot also makes a difference. Some powders are more corrosive then other powders. Pyrodex RS is about the worst. Some of the powders like APP or Triple Se7en are a little more forgiving but still needs to be cleaned.
If you are shooting a traditional rifle, I swab the barrel with pure isopropyl alcohol. Also if you are going to leave the rifle loaded, be sure to be careful of the moisture forming in the barrel. Here is where I do store the rifle muzzle end down on a piece of cloth. That way any moisture that MIGHT form moves away from the powder charge. Also keep the temperature you store the rifle for the night is approximately the same as what you hunted in. Also be sure to mark the rifle and warn all around that the rifle is loaded.
I had bad experiences with misfires when I tried to store them over night. Others though have no problems at all. But when I load fresh in the morning I know that rifle is going to fire that day.