I always thought that if I had an SSL connection there would be no MITM attacks. Now it appears that isn't true (see comments in this question Is it okay from a security perspective to read foreign (untrusted) cookies in a trusted network?)

I'm still unsure how it works and whether each browser needs to install a certificate, but it sounds like a proxy on your LAN connection either redirects the domain (I probably misunderstood) or uses an alternative certificate (doesn't the cert need to match the domain? I'm still confused).

Would it be possible to check if I am connected to the true site? It would be helpful too if you can explain how the proxy can create a valid cert for a domain it doesn't have the real cert/keys for. (I know this is two questions but both can potentially be explained by one answer.)