Twitter can help you find accounts to follow by directly recommending new accounts that may be of interest to you. If you see a recommendation that interests you, click on the username to see more information. To follow them, just click the "Follow" button to get their Tweets in your home timeline. More information about following can be found here.
Suggestions will appear on the left side of your home page, Connect and Discover pages, and profile pages on Twitter, as shown in the image at the bottom of this page. Below is an explanation of which types of suggestions show up where.
Twitter's staff does not editorialize which users show up in suggestions. Twitter search uses an algorithm that determines highly personalized suggestions based on the accounts you currently follow, the accounts followed by the users you have chosen to follow, and how other users express interest in Tweets sent from these accounts. This should help you find the information you want to know (and some information that may surprise you) faster. If you're interested in Promoted Accounts, click here for more info.
Twitter's Troubleshooting pages for following issues have solutions to common problems.