The circuit show a crystal, not an oscillator. The third connection, the one to ground, is just the case. You have a crystal. It will work fine between OSC1 and OSC2 whether or not you ground the case. It can help to add 10 - 20 pF between OSC1 and ground, and also 10 - 20 pF between OSC2 and ground.
If you have an oscillator, they are usually square or rectangular rather than oval like a crystal. An oscillator has connections for power and ground, and an output which you connect to OSC1. You would then leave OSC2 open, and you don't need to worry about capacitors.