Usually, there are two different ways that you can do this. One is to go to the website of your bank or credit card--whichever place you want to pay the bill from. Somewhere at that site, there will be an option to pay your bills. If you aren't online yet, just try typing in the bank's name, followed by .com. So, for example, if your bank is Wells Fargo, their website is wellsfargo.com, and once you are there, you can set up your account, creating a username and password. You'll need a check, debit card, or credit card to do that, because they'll need your account information. Then, once you are online, you can find their bill pay option, and follow the instructions. Typically, you'll need to enter the institution's name (whatever company you need to pay the bill to) and address, then the amount of the bill and what day you want it sent.
The second option is to go to the company's website, whichever company you need to pay the bill to. Information for that website will be on the bill itself somewhere; so, for example, if it is a hospital bill, on the bill itself it will state what website to go to in order to pay that bill. Once at the website, browse around, and you should be able to find an option to pay your bills. You'll probably just need an account number (also found on the bill), and a credit or debit card of some sort to pay the bill with.
Either way, paying bills online is so much nicer and faster than sending a check through snail mail! It is deducted from your account immediately, saves money on stamps and envelopes, and a trip to the mailbox. Good luck!