Chemically. Digestion using Aqua Regia or Piranha solution are fairly common. Nitric acid with sulfuric acid is also used, basically you want a strong acid (or more) and a strong oxidizing agent. Now what are you analizing will determine what solution is right for you, more volatile elements like arsenic and antimony can have minor issues.
Ian linked really good procedures, I guess it comes down to what do you want to measure. If you're measuring heavy metals such as lead, mercury, cadmium, thallium, copper, etc, you can use almost anything since the oxidation state won't matter. With Chromium, arsenic, antimony, manganese, etc, you will likely end up with a mixture of both cations and oxyanions of these elements, so aditional work up may be needed to have them all in the same oxidation state. With chromium for example, if you want to do a flame spectophotometry you may need to dilute a part of your digested sample and add a reducing agent, since most chromates are very insoluble. Ideally you should be able to have all of the analyte in solution to measure correctly.