In a research they calculated (by a microscope) the efficiency of EGFP-tagged plasmid, but they didn't mention the way of calculating. What is the possible ways to carry out this procedure?
You could use IMAGEJ to calculate the fluorescence intensity. There is a very comprehensive tutorial in their website. The software is free. There is a ton of stuff you can do with this software.
Do you mean checking the transfection efficiency? There are many ways even with microscope. We prefer to use flow cytometer or a fluorescence cell counter. By microscopy, you can use area coverage but not very reliable. One may also do Hoechst staining GFP colocalization but you need to have a software to do that. Also, it may be hard when you have cells in clumps or colonies. With cell suspension in flow cytometry and fluorescence cell counter, you will get more accurate counting.