Go to ‘Arctoolbox’.
Then Click on ‘Data Management Tools’,
Click on ‘Projections and Transformations’.
Click on ‘Feature’. Here you will see two tools – 1. Create Spatial Reference and 2. Project.
Click on the tool ‘Project’. A new window with title ‘Project’ will open.
Here you have a small form to fill.
In the ‘Input Dataset or Feature Class’ – input your shape file or other dataset you intended to transform the coordinate system.
In the ‘Input Coordinate System (Optional) – here your files existing coordinate system will appear.
In the ‘Output Dataset or Feature Class’ – normally it saves the output file in the same folder and with same name of your input file and adds number with it. You can change the name of your output file.
In the ‘Output Coordinate System’ – select your coordinate system that you want to have for your input file.
Normally you don’t need to do anything to ‘Geographic Transformation (optional)’ box.
Now press OK.
When everything goes fine, you will see a new window with name ‘Project’ that tells you ‘Completed’. Close the window and be happy at this stage. But prepare yourself for further works.
Thanks go to: Thank You Miss Kirsten Erickson for the great tips (Martin-Luther University Halle-Wittenberg, Germany), and solving the problem that was hanging on our heads.