You'll find great tips over on the Rehab and Rescue thread but since you asked here, I'll give you a quick run down of what I do. First, I vacuum the bag out. You probably don't have to do that since you've owned your bag for a while but I buy lots of bags on ebay and sometimes they come with surprises in the pockets.
Next, I rinse the bag under warm water, gently scrubbing it with my fingers and I apply dish soap directly on any dark spots, massaging it in. Sometimes the spots come right out, sometimes not. But I always try. I wear gloves so I don't turn my hands fancy colors. After a minute or two, I plug the sink and add dish soap and then I soak the bag for about 15 minutes. I scrub it again with my fingers after 15 minutes. I then drain the sink, fill it again with just water, and soak for another minute or two. Then I thoroughly rinse the bag under warm water until all the soap is gone. I let it sit in the sink to drain some of the water off and then I pat it dry with paper towels, stuff it with dry cloth towels to shape it, and I position it appropriately to dry, sometimes laying it flat, sometimes hanging it, depending on the style of the bag. My bags usually stink when they're wet but don't worry, this will dissipate as the bag dries.
If the bag has thin leather straps or other details, I often condition those after just a few hours because they dry much faster than the rest of the bag. For your city bag, I would condition the strap after maybe 6 hours, give or take. Your home environment will affect how fast the bag dries. I will usually apply the first coat of Leather CPR to the entire bag while it's still somewhat damp but not wet. I don't let the leather completely dry anywhere on the bag without at least one coat of conditioner, I don't want to risk the leather cracking.
I then apply one coat of CPR about every 24 hours until the bag is well conditioned. As a final step, I add Blackrocks, which adds a beautiful finishing touch to the leather. That's it!
This isn't an exact science and many of us have our own techniques. In my opinion, the most important thing to do is not allow the bag to dry without conditioning. One time I poorly timed when the bag would need its first coat of conditioner and I wasnt going to be home in that several hour time frame so I conditioned the bag while it was more wet than I usually like. It turned out fine!