If you hold NEO the token you will receive is not NEO but GAS. GAS can be traded on many exchanges.
All you have to do to get your GAS is to hold NEO in either your desktop wallet or on one of the exchanges that will give GAS for the NEO you hold.
Unlike some other staking coins you do not need to keep your NEO wallet open all the time.
To claim your GAS all you need to do is send your NEO to yourself, I think the Neon wallet can do it automatically.
This is how to claim GAS in the neo-gui wallet http://docs.neo.org/en-us/node/gui.html#claiming-gas

Two of the exchanges that give GAS are Binance and Kucoin.
Some more resources about NEO here.. https://www.reddit.com/r/NEO/