Entry level roles in Banks are generally for Clerical and Probationary Officer(PO) posts. The minimum qualification is any Bachelors Degree (Graduation). Specialist Officer (SO) recruitment is for experienced staff.
Public Sector and Private Sector banks have different processes for entry level recruitment.
a. Public Sector: IBPS (Institute or Banking Personnel Section) conducts the assessment and selection of personnel for Public Sector Banks, SBI, Associate Banks of SBI, RBI, NABARD, SIDBI, some of the Co-operative Banks, LIC and Insurance companies. IBPS exams are mandatory for entry into Public Sector Banks.
b. Private Sector Banks, Foreign Banks and other Banks which do not participate in IBPS: Each bank has its own recruitment process. Keep checking Individual Bank Career pages, newspaper ads and announcements. The big Private sector banks also conduct joint programs with educational instiutes like Sikkim Manipal, Amity Global, NIIT etc for a training cum recruitment like Axis Bank Young Bankers, ICICI PO program etc.
For entry into a Bank, good skills in maths and analytical ability is needed. You need to do plenty of practice. There are numerous Coaching Centers providing coaching for Bank exams. Enrolling in these is advised as will learn from experts. Quite a few are listed at https://www.addmylearning.com/search/jobs-upsc-ssc-exams-coaching-courses/15/bank-exam-courses/26/
All the best for your success.