Generally any smartphone will use two wireless ways of connecting to the Internet, one is WiFi and the other is cellular. With WiFi it's a matter of having a broadband connection at your home (cable or DSL) and a wireless router; with cellular that requires you to have an active account with a cellular service, such as AT&T or T-Mobile. A computer can be helpful in certain situations but it's not necessary, your phone has its own online connectivity.
But this is just a very generalized summary, please provide more details about your situation and what kind of problem are you having getting online?
-- Do you have a broadband service provided by an ISP to your home?
-- Your profile indicates you have a Tracfone, a service tied to Walmart. They have multiple contracts to use other cellular service networks, do you know which one your account is with? (AT&T, T-Mobile, Verizon)
-- What phone model do you have?