Actually you mine it with only the VPS (as a matter of saying) because is not real mining where computational power is involved.
Idena mining is actually about running an Idena node, which is preferably to be run on a VPS due to the stability, and validating your identity once per cycle (the cycle last for 12 days now).
Idena client is only use for validation, making flips, sending and receiving coins. Apart of this the client is most of the time turned off.
There is not much to explain about "the mining", you just turn it on from the client (you have a button) and that's it. If you run the node on your PC you'll need to keep the client/PC on, if you run the client on VPS, you can turn off your client.
It seems simple to run Idena Node, but I don't know where to start to run Idena node, do you know the article that can be used as a reference to run Idena node?