Q:

How do I clean gold and silver ornaments? 

I heard, We can clean silverware using backing soda and hot water.  I tried this but it wasn't of much help.  Is there an easier way to clean them? 
not to be confused with -polishing the ornaments

A:

Seltzer water(carbonated water)
Put your ornaments into seltzer water for around 5-10 mins and brush them.  Ex club soda or coke
House hold dish wash soaps
Soak the ornaments in warm water for 5 mins and scrub with toothbrush using dish washing soap liquids. 
Using toothpaste
This is very common method and I've used many times.  Just apply tooth paste and leave it for a minute.  Then scrub with tooth brush and rinse. 
Ammonia and Vinegar
I heard they are also good cleaning agents, But I have never tested and not sure how frequently we can use.  You can use it on your own risk.  I am sure these will affects the ornaments which has pearls and stones with glues.  
Mouth freshener Listerine
I have tested this also and worked very well.  Just put your jewelery into the liquid and scrub with tooth brush after 15 mins.  
Tamarind
Indians knows the benefit of tamarind.  This is widely used to remove thick and strong tarnish.  Just soak the gold in tamarind water for 10 mins and brush it. ( off topic, rub some tamarind on brass to make it sparkle like gold.) 

TIPS:

If your ornaments has gemstones (rings, pendants, etc) avoid using warm or hot water or chemicals.  This will not affect the metal but loosens the adhesives glued in.  
Avoid brushing silvers with brushes having hard bristles and long time, It will scratch the silver.  

P.S: Your method of baking soda and hot water method is not recommended.  It involves more work and care.  Usually aluminium foil has to be placed under or wrapped.  This is being done to move the oxidation formed on the silver to aluminum foil, Else this method will not be effective and may turn the ornaments black.  

A:

Silver tarnish can be removed electrolytically by putting the silver object in an aluminum container (e.g. an aluminum foil pie plate) with water with baking soda dissolved in it.  The silver must be in contact with the aluminum and completely covered by the salt water.  Warming gently speeds this up.  It should be cleaned as you watch in less than a minute! 
This sets up a "battery" (well, cell is the singular) and short-circuits it, causing the sulfur in tarnish to migrate to the disposable foil pan (which looks mottled gray afterwards).  It won't do much for cleaning skin oils and other dirt, though; you'll need a toothbrush and elbow-grease for that. 
Caution: do not use on niello or lacquered articles, as it will damage the inlay and finish.