At home, I would consult the documentation. Or if the router has a config page (192.168.1.1 or the like) that you use to set it up, check there for the ESSID. That certainly is a reasonable guess, but if you're the admin, you should find out anyway.
Additionally, for you home network security, you should change it from the default ESSID and should also disable broadcasting the ESSID. Change the default password of the router as well. Once you get it all up and running, you might look into WPA encryption keys and limiting connections by MAC address. And physically locate the router as close to the middle of your house as possible. Unless you don't care if someone might leach your connection without your permission.
My brother lived in an apartment and couldn't figure out why his network was so slow until I audited his network and found a neighbor was hosting a Warez site on his connection...
At random internet cafes they usually broadcast their ESSID (your connection gui should list available networks in your area). If not, ask the clerk. Sorry I can't be of any more help, but I don't have any linux wireless clients for home, just my wife's work laptop which is XP.