I have an object in one blender file that I would like to transfer (import) to the other blender file. Please help with the advise of how to do it.

If you want to import an object from one file into another use Blender’s library functions (see also the wiki:

Just open the file you want to import from with Shift-F1, select the desired object and load it. By default this will append the selected object etc. to your current .blend file.

If yuo’ve got several objects - among several more - it would be better to group them. Then append the group as Doubled said. You can ungroup it later, if you want.

For sure! And you can also select multiple objects with RMB and append them without grouping. It just depends on what your needs are.

Many thanks to everyone! It worked.

Thanks. I didn’t know that.
For some reason, multiple selection seemed to work for me only when grouping.