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The wifi should kick in automatically if you have it enabled. You should also see the little wireless icon in the status bar when you are using wifi.
Is the wireless connection secured?
Yes it is. I have a DLink G router. I bought the switcherpro widget. Turned off 3G through that and turned on wifi. The video uploaded to youtube. Very weird.

It might be the n protocol as others have mentioned.
I'm using Verizon's FIOS wireless router/modem (I think it does n too) and have not had any issues with both of the Droid X's that we have. Then again, the Mrs. was using the 3G for a while at home since she didn't know what the wireless toggle did.
I do notice that my wifi icon disappears from the status bar but then comes back after unlocking the phone.
that might be in part to battery settings