I would suggest building construction fields, as usually building construction covers most of the aspects of civil engineering (depending on the type of project).
You can go up to any construction company and ask them that you want to work with them as a trainee. May be you will be needing an internship letter from your university or college. Working with private construction firms is a good idea as most of government projects are very slow, moreover, your presence will not be noticed there.
- You can get training about how the actual work is done in the field.
- You will learn the importance of different lab and field tests
- You must learn also the estimation and quantity survey.
These are my ideas and suggestions only based upon my experience and learning. It would be better to consult someone senior to you, working in the field presently, in your area.