The "Network" your phone is on is your carrier. Whatever phone company provides your service. (i.e. Sprint, Verizon, AT&T, T-Mobile, etc.)
On most phones you can find the info in the the phones settings.
Go into "Settings" then scroll down to "About Phone".
Next Tap would click on "4G Settings" (or 3G if you have an older phone).
The first thing listed should be "Network Provider".