Unless you have Set up a WiFi Internet Connection using the Network Icon as explained in Absolute Beginners - A Guide to tweaking Easy Mode with wizards, the wireless connection doesn't start automatically. In most cases, this can be fixed easily as set out below.
If the steps outlined below don't always work, in other words, if you can connect manually but have problems connecting automatically on boot, also try following this wiki article.
The above didn't work for me as there was no properties button. If this is the same with you try this:
If your Eee fails to connect on startup or is very slow to connect, try following the instructions in this forum thread