Payroll system in DBMS. I don't know wha...

Firstly you need to determine/state whether you are using a database application, such as Access, MtSQL or MS SQL and programming them to do create this application, or are you using a programming development tool such as Visual Studio, ASP.NET, PHP or the like, as the solution and guidance will be different for each.
In terms of the data design, you should store the data necessary to identify each employee uniquely and each data point per employee needed to calculate their payroll. You should then store the generic (applys to all employees) such as tax rates, in separate tables and call on it to calculate wages and other paystub data.
For instance, the employee first and last names and tax ID should be a sufficient unique identifier. Create a table for just employees, their names, tax ID, start date, schedule, pay rate, number of deductions, direct bank payment data, etc., and whatever else you decide you need for each employee. You can calculate their wages by multiplying their rate by their schedule and applying the appropriate tax rate and medical/witholding deductions as you go, so calculated data does not need to be stored and consume database space. 
You'll likely need a separate table for common data such as tax rates, one for deductions/witholdings, one for holidays, one for vacation accrual rates, one for medical rates, etc. This data if common to employees does not need to be stored per individual, as that would cause redundant replication of data. If the employees are on an hourly rate, rather than a set salary/wage, then you'll need a table of worked hours per employee, akin to their timesheet data. If you use a timesheet/timecard, the entering and storing only the totals and keeping the physical timesheet for backup records should suffice.
Once you design and populate your database as suggested above, then it's a relatively-simple task of calculating the computed paystub data and storing the salient resulting datapoints for the record.
Consider a reporting application, such as Crystal Reports, for your printing needs, as its far easier to configure Crystal or similar product to format reports, paystubs, checks, etc., than coding these from scratch.
Hope this helps.

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