It is difficult to bleed brakes with one person. If doing it by pumping the pedal the objective is to push the pedal down and hold it that way while a 2nd part releases the bleeder and allows fluid to squirt through and then tighten the bleeder to seal the system so the pedal can be released and re-pumped up to apply pressure again. If there is not two people, one person can do it by attaching to tube to the bleeder fitting that is long enough to reach into a container that will be thrown away partially filled with brake fluid so that bleeder can be opened and then some one pumps the brakes. The idea being that when the pedal is pushed down fluid squirts out and when the pedal is released and allowed to return it will return faster than it takes to suck the now partially filled fluid back into the system so you can eventually pump enough fluid through by your self thus eleminiating air being sucked back in. Then you can go back and shut the bleeder while the tube is still emmersed in contaminated fluid.
Or a power bleeder.
Years ago I made an electric power bleeder I can just turn on and it takes care of bleeding each brake line by itself. All I have to do is open the bleeder then close it.
If you have a brake line that is full of crap, it sounds like some where along the line some one did it wrong.
Brake fluid absorbs moisture given a chance so it sounds like air got into the line a long time ago and is still there.
The solution is to pump fluid through it until it is clear and hope there is no further damage.
That has worked many times in the past.
But Water causes rust and rust will screw up a wheel cylinder with drum brakes or a caliper with disc brakes.

 

Apparently, no matter how much I bled the left-rear brake, I was getting nothing but bubbles, even with brand new brake fluid completely present in the lines now. I found where the air was getting sucked in the system. There seems to be a leak in the left-rear cylinder, I haven't taken a real close look yet because I have to clean all the dirt and grime stuck behind there, but that should have given me a clue when it started leaking in that area as I kept pumping brake fluid through in the process of bleeding, as the other rear wheel cylinder seemed fairly clean. I'm hoping it's just a lose bolt where the line meets the cylinder, but if it's the rear cylinder, I saw it was suggested to replace both sides. Does someone sell whole rear-brake assemblies, including the cylinder, shoes, and springs pre-assembled? Or do I have to get the parts separately and put them together myself? I figured it would be easier to just replace the whole assemblies on both sides than putz with the multiple parts.

 

Thanks uncljohn, apparently I did the whole procedure right, just found a leak explained in my subsequent post below.

 

I found the cause for my confusion, my interpretation of orientation, when it came to the front, was backwards, so yes, you were right. I was seeing it your way, but I was calling the right and left wrong (instead of from within the car, I was stating it as if I were facing the car). Again, sorry if I sounded I was doubting you when you were trying to help.

 

A good question. I never thought of whole assemblies all preassembled.
I grew up rebuilding drum brakes. When disc brakes arrived it was a mystery, and expensive.
As it turned out it was duck soup except for the emergency brake which can be tricky.
I don't know how Saturns are set up mine has 4 wheel disc.
You can not buy parts pre-assembled. Dang good thought though.
Looking at all the bits and pieces you will find that they genrally are re-usable. The springs, the washer things, the pins etc. Generally just purchasing the brake shoes and a rebuild kit for the cylinder or a whole new cylinder is all that you have to worry about. Well that and getting it apart and back together.
Buying a new cylinder is an option. I have also rebuilt the one on the car by purchasng a kit and diss-assembling things and using something on the order of 280-300 wet dry sand paper and brake fluid and my finger, sanding the inside of the bore of the cylinder smooth was all that was required and then install new parts. But a new cylinder is a short cut to finishing faster. Personally I work with the philosophy of if it ain't broke don't fix it. If only one side leaks, fix the one that leaks.
You will need a brake spoon, used to adjust the brakes after rebuilding them although you can get away with using a flat blade screwd driver.
There are tools available for removing the springs. I use a combination of vice grips and a fairly large phillips (+) screw driver to help in taking tension off of the parts so the springs will come out or go back on.
A new vocaublary of swear words helps too,
Hine, do one at a time. So if you screw up, you have the other one to look at so you can see hot the bits and pieces go.
I have rebuilt a lot of them in my life. I can almost do it blind folded. It is a pain in the patooie. If this is your first time.
By a book with instructions. It does help.
Otherwise good luck
A note, why would I rebuild a cylinder rather than replace.?
Rust.
If it looks like I am going top break a brake line to the cylinder I won't touch it and just rebuild the one on the car.
Running new brakes lines is not a place I would rather go to.