After disassembling, I hit everything with a degreaser/cleaner. I like 409 cleaner for this. I scrub with bronze wool. I avoid steel wool because I like the softer, coarser bronze wool much better. I actually don't use steel wool on anything bike-related, come to think of it. I stick to bronze.
I also take the components to the bearings/nuts/races/spacers and soak them in a cup of 409. I use a string to keep them in the order they go on the bike, as well as keep them together. I clean them together and do not separate the string until I'm ready to reassemble later. This helps keep everything in order. After finishing the chain ring, it looks nice and clean, as shown below. This is a skip tooth Schwinn chain ring.
Next, move on to the crank arms. Degrease with the bronze wool and 409, then hit them with bronze wool and WD40 to remove the rust. You can alternatively soak in Oxalic Acid for rust removal. You have to degrease first either way. I did these with the bronze wool since I didn't want to mix up a soak just for this part tonight. As you see below, it came out just fine.
Then I head back to the frame and begin working on the bottom bracket cups. For these, I use a paper towel soaked in 409. I do NOT use bronze wool, steel wool or anything particularly abrasive. It is very important not to score the inner surfaces of the cups up, since their smoothness will help ensure smooth pedaling. I use a paper towel and hard work instead. It comes out nice and clean.
Next, I hit up the outside of the bottom bracket region. This particular bike was caked in old grease and sand mixed up. They formed a tar-like substance. I used a Dremel cleaning brush to remove the caked substance. The picture above clearly shows that external cake, but below you see it's just about gone.
Now, it's back to those soaking vitals. Pull them out and wipe them down. Even tough grease gives way with a soaking and wipe down. I use a soft cloth for this usually, but tonight I'm down to paper towels. Paper towels annoyingly tend to leave little pieces to pick out of the bearing cages. The soft cloth is better.
Once they are clean, I liberally coat them in WD40 to displace the 409, and let them soak in WD 40 overnight in the cup. This keeps out the moisture. When I'm ready to reassemble, I'll use a good quality lithium grease on these.
Here you see a little progress shot- you can start to see it, but it still has a ways to go.