Extraction of monosodium glutamate (MSG) from kelp
Monosodium glutamate was originally discovered by Kikunae Ikeda using a simple aqueous (hot water, namely his soup) extraction of kelp that was later refined and patented.  That particular species was Laminaria japonica. This along with a more detailed description of the original process and the history of MSG processing is given here.

The sulfuric acid treatment and precipitation process described therein certainly cannot be simply and safely done at home. The main purpose of that is to convert other compounds (e.g. glutamine) into glutamate to give higher yields of pure MSG for commercial usage. As stated in this Wikipedia article:  


  "MSG is freely soluble in water",


so, as Ikeda enjoyed the water extract, I would suggest trying that first.  If you need a more concentrated extract, simply let the water dry.  I wouldn't use more than mild heat, maybe an oven on very low setting with a fan, to prevent degradation of your product.

An interesting side note, stated in both sources above, is that Ikeda's discovery of MSG was also recognized as the discovery of a new flavor at that time (in addition to sweet, salty, sour and bitter).