How do I wake a sleeping server?

Try to connect from Minecraft. The attempt itself wakes the server up — you will be disconnected with a message saying so, and can reconnect a moment later once it has booted.

You can also press Start on the server page, which does the same thing without the disconnect.

Booting takes longer the first time a particular version runs on a machine, because the server software has to be fetched before it can start.