There are a variety of ways to set up a business to accept credit cards.
For small volume merchants, there are simple devices that can be used in conjunction with a business account through PayPal or Square which allow you to use a cell phone or tablet to accept cards through those services. They charge a small fee per transaction and require your business to have an account with them. These services generally do not have long term contracts and the hardware is either free with a promotional code or very low cost.
For most merchants, a business account will be preferred, and you can get one through your current business bank. They can put you into contact with their preferred vendor for credit card/debit card transactions (this will be a third party, not your bank, and you will be setting up an account with them, these accounts are usually multi-year accounts with somewhat punitive cancellation fees, and require that you purchase equipment, so make sure to read the contract carefully before signing or agreeing to anything).
You can also contract directly with an "ACS Provider" - similar to the provider that you would work with through your business bank, and the same cautions apply.
(I do not mean to imply that these contracts are bad, or somehow they are unfair, but I do work with a lot of merchants and I know that one of the biggest complaints is that once you have signed with an ACS provider it is somewhat costly to cancel - so it is worthwhile to shop around and get multiple quotes before signing on to the service, and again, make sure you read and fully understand all of the terms before signing).