As you want to do check Online balance of your account which is in Bank of America and for the same asking for process to do login , so I am telling same here

Go on Bank of America official website

Click on online banking option which given under banking section

By click there you will land on online banking page

Over there to login you need to click on sigh in option given on the top side

By click there you will land on sigh in page which look like following image


Services
Personal

Merrill Edge Investing
Merrill Lynch Wealth Management
U.S. Trust
Personal Information Management Services (PIMS)
Privacy Assist®

Small business

Remote Deposit Online
Merchant Services
Small Business Online Community
Automotive dealer services
Marine dealer services
Recreational vehicle dealer services

Businesses & institutions

Asset-based finance portal
CashPro online
Institutional trust, investments and custody (Account Management Online)
Leasing portal
Mercury