You can get away with skipping the brass cleaning step for a little while. Especially while first leaning to reload. At a minimum you can wash your brass with Methyl Hydrate. Eventually you are going to need a solution for cleaning large amounts of brass.
There are three popular methods.
Tumbling with Media
This involves turning or vibrating the brass in a walnut or corncob polishing media. The machines are usually loud so make sure you run it in the basement or the garage, or put it on a timer and let it run with no one home. Tumblers do a very good job of cleaning the brass and the media lasts quite a while. Once the media gets old, it will get dusty and dirty.
The Lyman 1200 Auto-Flo Tumbler is a great product. It's a vibratory tumbler with a media sifter built in.
Another option is the Dillon CV-2001 and you will need a media separator
Ultrasonic Cleaners
This is my personal favourite. The brass is in a bath of water and soap, or a chemical cleaner. A transducer is used to cause micro cavitation (bubbles) to clean the brass. Dish soap works well, but a brass cleaner like Lyman's Case Cleaner will have the brass looking new after just 20 minutes. The device makes a bit of noise, but with the radio on you won't notice it.
Once the brass is clean, you can let it air dry. I usually have 3 batches of brass, one batch is dirty, the second is drying, and the third is dry and ready to reload. I run the ultrasonic while reloading to make sure I always have clean brass.
The secondary benefit is the Ultrasonic cleaner is great for cleaning gun parts. Barrels, revolver cylinders, and even the whole gun if you like.
Look for an article soon that covers gun cleaning.
Steel Pin Tumbler
The brass is tumbled with water and small stainless steel pins. The brass comes out looking brand new and then needs to be separated from the pins and left to dry.
I have not used one of these. The initial price is high, but the media lasts a long time. I'll add more information here when I can. The Frankford Arsenal Unit is quite popular. Lyman is releasing one soon.
Email me at chris@rougeriverarms.com if you have any questions or comments.