@arpthark
Everyone was taught in a different manner, so, as with most things in this field, there is not one official way to do it. You learn to use the tools to do some specific tasks then you are expected to figure out how to get the tools to do what you need.
My procedure actually uses a different filler, which is this funky bismuth alloy called Wood's Metal. It is available by several commercial names, each being a slightly different concoction. The brand *I* like is called Cerrobend. And it is probably nastier to work with than lead or pitch, but it works better for me. ($1 to Ian for pointing me to this product.) Cerrobend has an advantage over other fillers. Pitch is soft, so it tends to deform the most when bending tubes. It is also nasty to get out of the tube. Lead very slightly contracts when it cools, so it fills the tube sort of loosely and can cause ripples when bent. It is also a lot harder to bend tuba-sized tubes using lead. It can be hard to fill a tube without air pockets, which can collapse when bent, causing a kink in the tube. Lead takes a lot of heat to melt so you can pour it down a tube.
Cerrobend has a very low melting point, and it actually *expands* a tiny amount when it cools so that it fits very tightly to the tube wall. It is easier to bend than lead (but not quite as easily as pitch). But it requires using a mask and gloves, and you have to ice-water-quench the tube using very specific instructions or it will not work correctly. It is finicky stuff and very toxic. Melting it out is very easy and clean.
Lead is the easiest for most people to find and work with, but it too is toxic to touch or breathe fumes. (It's a slow-acting sort of toxicity, so I usually just wear one of my N95 masks and wash my hands, arms, and face when finished.)
What I do (which is different than what others likely do):
I coat the inside of the tube with motor oil. I let it drain out to the point of there being a very slow drip. I tightly cork the small end of the leadpipe. I have a 5-gallon bucket of sand that I stick the corked end of the pipe into about a foot deep so that there is no way the tube will tump over on me and spill the molten lead all over my feet as I scream and dance about in pain.
I have a hot plate burner and an old 2 qt. saucepan for this, along with a steel ladle for pouring molten metal. I put the pot on the burner and turn it on. I place a 5-pound ingot of lead (or an already used "pancake" from a previous melting) in the pot and let it heat up and fully melt. The pot has been hammered over an anvil to have a pour spout that is sort of long and narrow to work with small diameter tubes. If I only need a little lead I will use the ladle, but for a leadpipe, I will pour directly from the pot into the pipe.
You must pour slowly to prevent any air pockets from developing. Air pockets can cause kinks when bent, as stated above. MORE IMPORTANTLY, though, is that when heating the pipe up to remove the lead the air pocket can "burp" a mess of molten lead onto your skin! So fill the pipe using a slow but steady flow of lead. Fill it all the way until it is just doming up over the top. It will contract down into the tube about a quarter inch. Let it cool for a long time. I usually leave a pipe like this for an hour or so. If it is still warm to the touch the lead in the center might still be soft. Leave it until it is room temperature!
Once you have bent the tube a little, tap down the ripples — gently! — until it looks reasonable. Bend a little more, tap a little more. Keep doing this until the desired shape is achieved.
To remove the lead I hold the new leadpipe with the large end facing downwards, and I heat the end until the lead is running out, and I keep the flame hot and constantly moving to melt it out all the way around, working my way toward the small end in three to four-inch segments. Do not allow the lead to splash. Keep the pipe end very close to the surface of the drained-out lead because sometimes solid hunks will fall out suddenly, and skin grafts sort of suck.
Eventually, you will have worked all the way to the small end. (You wore heavy cowhide gloves. Right? And you used some sort of tongs that will not mar the finish of the tube. Right?) Once that is done, remove the cork (if it is still even there) and heat the tube again to burn out the oil and release any remaining lead. Let it fully cool again. Run some hot water and get a snake and some DAWN (which will help to remove any oil residue) and scrub that puppy out really well. Put it in a container of straight white vinegar to soak for a little while to eat out the rest of the junk inside. Get a light and check the inside to see if it is CLEAN. If there is lead remaining estimate where it is with a Sharpie on the exterior and hit those spots again. Repeat the washout process. Check it again. Get it clean!
Feed the leftover lead to people you dislike.
Okay, save it because it is not cheap and can be reused many times. I drain it back into the bent-up cook pot I melt it in. It will not adhere to good stainless. Once it has been fully collected leave it alone to cool. Once it is cool you can pry it out of the pan and put it into a ziplock baggie for storage.
All this applies to pitch, too, but the washout work is tedious as the pitch is NASTY to remove. Cerrobend is actually designed to be a bendable filler so it has all these cool characteristics, one of which is that it comes out fully with no real fuss or mess. Again, it is toxic and a PITA to use. If you choose to use a bismuth alloy like Wood's Metal you must read and re-read the instructions, which have more steps and must be followed correctly or you will have problems.
Good luck!