I have all my customer details in Microsoft Access. I want to transfer all this data to FileMaker Pro. I hope there is a way to do this. If so please help me.
You have basically two options (without resorting to any third party tool, besides ODBC):
Use intermediate "common import/export formats": Export data from all the different tables in Access in a format that FileMaker Pro can immediately import, then import the exported files from FileMaker. The safest format is normally CSV --comma separated values--; although it won't work with FileMaker if you have data with line-feeds or carriage-returns inside. You can also try Excel as an intermediate export format (with this format, you may have some limitation if you have long texts). Check: Introduction to importing and exporting data (Access) and Bringing data into FileMaker Pro - Overview and troubleshooting.
Direct import through ODBC: Directly import the tables from FileMaker by means of an ODBC connection**. When you install Office, you normally get ODBC controllers installed by default, so, if you have Access installed in your computer, you're very likely to have ODBC controllers as well. Make an ODBC connection to your Access database, and use it from within FileMaker to import your tables. Check Querying an ODBC data source from FileMaker Pro.
FileMaker can import table data from Access (or other databases). It cannot import table relationships (or foreign key relationships) or primary key definitions, null/not null constraints, index definitions or check constraints. All these metadata you'll need to transfer "by hand". The Access database documenter can help you get most of it.