To tell if O2 is ionic or covalent (also called molecular) we look at the Periodic Table that and see that O2 is made up of two non-metals. When we have a non-metal and a non-metal the compound is considered covalent.

Because we have a non-metal and non-metal in O2 there will be no difference in electronegativity between the non-metal and non-metal. This difference results in an electron(s) being shared between the non-metal atoms..

---
Helpful Resources

Metals, Non-Metals on the P- Table: https://youtu.be/OoooStZQHdA
Ionic, Covalent, & Polar Covalent: https://youtu.be/OHFGXfWB_r4
Electronegativity for each element: https://en.wikipedia.org/wiki/Electronegativity
---
Because we have a combination of a non-metal and non-metal O2 is considered a covalent compound.

For more chemistry help, see http://www.Breslyn.org.