I don't think you can. a gdb file is a geodatabase that contains feature classes. A mxd is a map document which has references to data-on-disk or web services. References, not the data itself so you can't export data out of an mxd file.
The Feature Class to Feature Class tool? Right-click the target geodatabase in ArcCatalog and use the Import option? Right-click the feature class (in ArcCatalog) and use the export button?
Have a look at Consolidate Map—Help | ArcGIS for Desktop. There's a CONVERT option that should convert all your map's data into a file geodatabase. I haven't used this tool personally so am not 100% sure how it will behave if you have "exotic" layers in your map, like rasters, network datasets, topology, etc. It's worth a shot, though.
Are you looking for tutorials Sarath on how to do some of these basics? There are a number of tutorials in this link that should get you going with working with data etc.
