Most email services will work on any phone regardless of which network it is connecting on, that means that in most cases you don't need to change any settings to access email after you put a different SIM card in your phone. However some ISPs (including Bigpond, Exetel and Optusnet) will not let you send email when used from a different network.
Although not a practical option on a small screen, Bigpond and Optusnet customers could try use webmail through the Bigpond or Optus website. Alternatively set up a free Gmail, outlook.com or Yahoo! email account, which should work just fine. Some customers have reported success sending and receiving Bigpond email through a Wi-Fi connection, however I wouldn't count on it and you're advised to set up an alternate Gmail, outlook.com or Yahoo! email account to use on your phone while you're away.
Using Gmail's SMTP server
If you have a Gmail account, it is possible to send email from your regular email account using Gmail's SMTP server.
Follow these instructions from the Lifehacker website for more details on how to do this: http://lifehacker.com/111166/how-to-use-gmail-as-your-smtp-server?tag=softwareemailapps
The drawback with this method is that Gmail will rewrite the "from"" field with your gmail email address whereas most people would rather have their regular email address shown here. However this post on the MobileRead forums shows how you can get around this restriction: http://www.mobileread.com/forums/showthread.php?threadid=4857.
More help resources from Apple
If you have an iPhone and you're trying to send email from an email address that normally sends through a network that blocks SMTP access from outside their network (such as Bigpond/Telstra or Exetel) and are having problems sending email refer to this information from Apple: http://support.apple.com/kb/ts1426