They feed the power generated by green sources into massive and expensive banks of batteries as part of datacenter-grade uninterruptable power systems.
They'd also have backup generators in case the banks of batteries ran down, and as longneck said in his answer, almost certainly have a secondary power feed coming in from "the grid," powered by conventional energy sources.
EDIT: Looks like I should source my answer, given that a number of people seem to think it's all handled with conventional energy at some point.
For a source on how this can be done, here's a little article on one of Apple's new 100% renewable energy datacenters.
The company had already announced plans to build a 20 MW solar array installation and a 5 MW fuel cell installation at the NC data center, which will be the largest private solar array and the largest non-utility fuel cell project in the country. Those projects are expected to provide 60 percent of the data center's electricity needs. The big news is that Apple is now doubling the on-site solar power capacity by building a second 20 MW array with the total solar power generation to now hit 84 million kWh per year.
The remaining energy needs of the data center not met by the on-site sources will be met through purchasing renewable power from local and regional sources.
So basically, between batteries, fuel cells, and purchasing "green power" from non-local sources, it's easily possible to power a data center with 100% "green" energy, and not rely on conventional "dirty" power at any point, possibly excepting a backup/emergency power feed based off the normal power grid.
And, just because this is who I am, I'll pose the question I always do regarding "green" [whatever]... how environmentally friendly do you think it is to manufacture all this green energy generation and storage equipment?
It's a rhetorical question, and the answer is it's very much not environmentally friendly.)