If you're behind a router, there's two things you need to do to be able to send dcc with AmIRC (receiving is always ok).
1) You have to forward the DCC ports to your computer running AmIRC. You can select these yourself with the last AmIRC beta, I recommend 1045-1055 (1 for each file being DCC'd simultaneously.
2) If you don't have a static IP or some kind of DNS address (or manually set your IP in AmIRC each time you're online), you'll have to run some script to tell AmIRC what your IP address is, otherwise it'll use your LAN one, and this won't work. SetTIADCC (on Aminet) will do this; set it to be run when AmIRC starts.
Note that software routers with conntrack properly set up don't suffer from 2).