Internet with my new blackjack 2 cellphone?

I just bought a new blackjack 2 phone today. My plan is the most basic one, besides having unlimited texting this month (for a rebate). I know when it comes to connecting to the internet, they make you pay. I was curious and went on internet explorer for a couple seconds... I did indeed connect. Now my question is.. am I able to connect to the internet through my own home internet connection, or any other means without using their "medianet" program. When I go on internet explorer right now am I being charged? Basically I need an overview of how ways in which i can connect to the internet through my phone.. thanks