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The cheapest way to call overseas is using your PC/Mac using a VOIP service. Here are some examples:
+PC to PC for free eg. Skype,
+PC to landline eg. Voip Cheap (you have to pay to top up though). You can do this via Skype also but you again, you have to pay.

Landline to landline/mobile:
+Using your normal landline such as BT is expensive and not recommended unless you are on a special package. Even then it is still more expensive than other providers.
+Using a PC there is JahJah which is free to some destinations.
+Calling cards - there are so many calling cards out there! Check all details before you buy as there can be connection charges, extra for calling from a payphone, expiry dates, minimum charges, etc. Advertised rates are seldomly the actual rate.
+Access number providers. There are a number of them such as Just Dial where you call an access number (different numbers charged at different rates depending on desination), then dial the desination number. eg. 2p/min 0844 838 5931 to call Japan/US/Canada/Europe.

Mobile to landline/mobile:
+Never dial direct from your mobile phone unless you are on a special package, it is VERY expensive.
+O2 and other providers have special international sim packages that give you x minutes of "free" international calls when you top-up. Exceed the free minutes however and it can be very expensive. Calls/texts in the UK are probably slightly more expensive than a standard non international package so make sure you weigh up the pros/cons of using the service.
+Again there are calling cards where you dial a landline access number (if you have inclusive minutes on your mobile contract this part could be free), and then you dial the international portion and credit is deducted from the card balance.
+There are services "virtual cards" where you "top-up" by texting to a number. Dialling an access number and then the international part is the same. I text "2japan" to 80041 for £3 credit and it costs 1.5p to Japan, 1p to US.
+There are some international PayAsYouGo sims such as Nomi mobile. They allow you to call directly to an international number without having to dial access numbers. The cost is slightly more ' 5p to Japan landline, 12p to Japan mobile, but it is a lot less hassle. Calls within the UK are also cheap when compared to O2/Vodafone/3/etc PAYG deals. If you have an unlocked mobile that takes sim cards I got given a stack of free sims for Nomi ' I can mail you one. Send me an email.

Hope the info is okay, it's a good starting point anyway!