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The best way to avoid international roaming charges is to start turning different things on your iPhone off right from the beginning. Data roaming needs to be turned off immediately, and this is going to be top priority. Start by going into Settings and then select General. Go into Network and find Data Roaming, making sure it is not set to On.
From here you will want to also turn off Enable 3G, as you are not going to be using that as often as you would domestically. Save the 3G network for emergencies and instead try to only access Wi-Fi, which may or may not have more availability when you are in other countries.
Push Notifications are going to have to go immediately as these access the internet consistently and you are not going to be able to interact with things like email and social networking sites from your iPhone anywhere near as much as normal. Push Notifications will not be useful at any point with this, so just keep them off the entire time unless you want to turn them on just briefly once you are securely connected to a Wi-Fi network.