Distributed
Synopsis
Slashdot has a quite geeky use base, it might be supposed, that a lot of them would be willing to use a browser plugin to access Altslashdot, if the incentive would be save the community, disable ads etc. Still, a centralised webhosting would be needed, e.g. to attract novices or to support rare browsers.
The idea is, that if a lot of users use a bittorrent--style decentralised hosting, running the centralised web server would be cheap enough to life off donations.
Technology
There is some discussion about a relevant technology already. See e.g. Could BitTorrent Be The Distributed Social Network People Have Been Clamoring For?. In fact, a rudimentary technology that would serve a static site exists already, e.g. btsync based web sites.
Surely, a lot od development would be needed. But the upside would be, that Altslashdot would be independent on businesses, dependent on users -- a good thing, as it would serve only the latter.