Networks behind NAT

BlitzMax Forums/BlitzMax Programming/Networks behind NAT

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Has anyone tackled getting a connection to multiple individual machines who are behind a NAT (address translation) as part of their router or whatever? I have been reading about it a bit and about how due to a limited number of available IP addresses NAT tries to open up the network packets and replaces their IP addresses with a single address, so that it then looks like the packet came from one place so you don't know how to get a packet to come back to the correct computer... how do you get around this? I seem to recall experiencing this issue on an IRC client where it would not allow my two computers to both be on the same server a the same time. (This isn't a question about IRC, it's about how to implement networking (over UDP probably) so that you can support multiple machines in a home network?