Cleaning your really dirty brass is not as tough as you may think it is.  First, fill up your sink with hot water and add some liquid dish detergent.  Put your item in the water and allow it to soak for a few minutes.  If your brass item is very dirty, allow it to soak for 30 minutes.  Wet a soft rag in the soapy water, and ring it out until it is just slightly damp. Using the rag, gently apply pressure and begin cleaning your object.  Use a toothbrush to reach the detailing and cracks in your object.  If the object is not as clean as you want it to be, make a solution on your own that will clean it even deeper.

First, get a lemon and cut it in half.  Remove the seeds, and squeeze all the juice into a bowl.  Using salt or baking soda, pour some into the lemon juice and stir until you have a nice pasty consistency.  This is a great brass cleaner.  Use a dry cloth to apply the pasty solution to your brass item.  Clean in the direction of the grain of your object, working it gently into the brass until it removes all the tarnish.  Baking soda and salt are both abrasives, so do not apply too much pressure.  Use a soft toothbrush to clean out the tiny crevices.

Remove all the tarnish completely and dry your brass well.  If you see any spots you missed, use some of your leftover cleaner and clean and rinse one more time.  When the item is completely clean, dry the item as quickly as possible.  Brass is known for retaining water spots, so you want to be sure no water is left on your brass object.