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You can tell whether a site is indexed by Google by installing the free Google toolbar from Google (an invaluable tool for those involved in site promotion as it shows Google Page Rank values!)
the fastest way to get spidered is to throw a couple of free adsense ads on your page.
G needs to index your page in order to show relevant ads. The first time you load the ads, you'll see a PSA. Then you can expect G will send a secret agent over to check you out pronto - sometimes within seconds.